BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Source author record

Sven Schewe

Sven Schewe appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Formal Languages and Automata TheoryLogic in Computer ScienceComputer Science and Game TheoryArtificial IntelligenceMachine LearningSoftware EngineeringSystems and ControlDistributed, Parallel, and Cluster Computingmath.OCRobotics

Catalog footprint

What is connected

33works
10topics
4close collaborators

Actions

Connect this record

Log in to claim
Open graphBrowse works

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

33 published item(s)

preprint2026arXiv

Optimal LTLf Synthesis

Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to realise as many objectives as possible from a given specification consisting of multiple objectives, especially for the case that they are not all jointly realisable. We first consider max-guarantee synthesis, which commits to a maximal set of objectives that we can a priori guarantee to realise. We then introduce max-observation synthesis, which maximises a posteriori realised objectives that may be incomparable on different executions. Finally, we present incremental max-observation synthesis, which further improves strategies by exploiting opportunities for stronger guarantees when they arise during an execution. Experimental results show that different variations of optimal synthesis scale broadly equally well, solving a large fraction of the benchmark instances within the given timeout, demonstrating the practical feasibility of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

The Complexity of Games with Randomised Control

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is assigned randomly every time the node is visited during a play. In this work, we study two natural variants of this where control of each node is assigned only once: (i) control is assigned randomly during a play when a node is visited for the first time and does not change for the rest of the play and (ii) control is assigned a priori before the game starts for every node by independent coin tosses and then the game is played. We investigate the complexity of computing the winning probability with three kinds of objectives-reachability, parity, and energy. We show that the qualitative questions on all variants and all objectives are NL-complete. For the quantitative questions, we show that deciding whether the maximiser can win with probability at least a given threshold for every objective is PSPACE-complete under the first mechanism, and that computing the exact winning probability for every objective is sharp-P-complete under the second. To complement our hardness results for the second mechanism, we propose randomised approximation schemes that efficiently estimate the winning probability for all three objectives, assuming a bounded number of parity colours and unary-encoded weights for energy objectives, and we empirically demonstrate their fast convergence.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

On Good-for-MDPs Automata

Nondeterministic good-for-MDPs (GFM) automata are for MDP model checking and reinforcement learning what good-for-games (GFG) automata are for reactive synthesis: a more compact alternative to deterministic automata that displays nondeterminism, but only so much that it can be resolved locally, such that a syntactic product can be analysed. GFM has recently been introduced as a property for reinforcement learning, where the simpler Büchi acceptance conditions it allows to use is key. However, while there are classic and novel techniques to obtain automata that are GFM, there has not been a decision procedure for checking whether or not an automaton is GFM. We show that GFM-ness is decidable and provide an EXPTIME decision procedure as well as a PSPACE-hardness proof. We also compare the succinctness of GFM automata with other types of automata with restricted nondeterminism. The first natural comparison point are GFG automata. Deterministic automata are GFG, and GFG automata are GFM, but not vice versa. This raises the question of how these classes relate in terms of succinctness. GFG automata are known to be exponentially more succinct than deterministic automata, but the gap between GFM and GFG automata as well as the gap between ordinary nondeterministic automata and those that are GFM have been open. We establish that these gaps are exponential, and sharpen this result by showing that the latter gap remains exponential when restricting the nondeterministic automata to separating safety or unambiguous reachability automata.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Alternating Good-for-MDP Automata

When omega-regular objectives were first proposed in model-free reinforcement learning (RL) for controlling MDPs, deterministic Rabin automata were used in an attempt to provide a direct translation from their transitions to scalar values. While these translations failed, it has turned out that it is possible to repair them by using good-for-MDPs (GFM) Büchi automata instead. These are nondeterministic Büchi automata with a restricted type of nondeterminism, albeit not as restricted as in good-for-games automata. Indeed, deterministic Rabin automata have a pretty straightforward translation to such GFM automata, which is bi-linear in the number of states and pairs. Interestingly, the same cannot be said for deterministic Streett automata: a translation to nondeterministic Rabin or Büchi automata comes at an exponential cost, even without requiring the target automaton to be good-for-MDPs. Do we have to pay more than that to obtain a good-for-MDP automaton? The surprising answer is that we have to pay significantly less when we instead expand the good-for-MDP property to alternating automata: like the nondeterministic GFM automata obtained from deterministic Rabin automata, the alternating good-for-MDP automata we produce from deterministic Streett automata are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially more succinct than minimal nondeterministic Büchi automata.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Enhancing Adversarial Training with Second-Order Statistics of Weights

Adversarial training has been shown to be one of the most effective approaches to improve the robustness of deep neural networks. It is formalized as a min-max optimization over model weights and adversarial perturbations, where the weights can be optimized through gradient descent methods like SGD. In this paper, we show that treating model weights as random variables allows for enhancing adversarial training through \textbf{S}econd-Order \textbf{S}tatistics \textbf{O}ptimization (S$^2$O) with respect to the weights. By relaxing a common (but unrealistic) assumption of previous PAC-Bayesian frameworks that all weights are statistically independent, we derive an improved PAC-Bayesian adversarial generalization bound, which suggests that optimizing second-order statistics of weights can effectively tighten the bound. In addition to this theoretical insight, we conduct an extensive set of experiments, which show that S$^2$O not only improves the robustness and generalization of the trained neural networks when used in isolation, but also integrates easily in state-of-the-art adversarial training techniques like TRADES, AWP, MART, and AVMixup, leading to a measurable improvement of these techniques. The code is available at \url{https://github.com/Alexkael/S2O}.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Recursive Reinforcement Learning

Recursion is the fundamental paradigm to finitely describe potentially infinite objects. As state-of-the-art reinforcement learning (RL) algorithms cannot directly reason about recursion, they must rely on the practitioner's ingenuity in designing a suitable "flat" representation of the environment. The resulting manual feature constructions and approximations are cumbersome and error-prone; their lack of transparency hampers scalability. To overcome these challenges, we develop RL algorithms capable of computing optimal policies in environments described as a collection of Markov decision processes (MDPs) that can recursively invoke one another. Each constituent MDP is characterized by several entry and exit points that correspond to input and output values of these invocations. These recursive MDPs (or RMDPs) are expressively equivalent to probabilistic pushdown systems (with call-stack playing the role of the pushdown stack), and can model probabilistic programs with recursive procedural calls. We introduce Recursive Q-learning -- a model-free RL algorithm for RMDPs -- and prove that it converges for finite, single-exit and deterministic multi-exit RMDPs under mild assumptions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurance

The increasing use of Machine Learning (ML) components embedded in autonomous systems -- so-called Learning-Enabled Systems (LESs) -- has resulted in the pressing need to assure their functional safety. As for traditional functional safety, the emerging consensus within both, industry and academia, is to use assurance cases for this purpose. Typically assurance cases support claims of reliability in support of safety, and can be viewed as a structured way of organising arguments and evidence generated from safety analysis and reliability modelling activities. While such assurance activities are traditionally guided by consensus-based standards developed from vast engineering experience, LESs pose new challenges in safety-critical application due to the characteristics and design of ML models. In this article, we first present an overall assurance framework for LESs with an emphasis on quantitative aspects, e.g., breaking down system-level safety targets to component-level requirements and supporting claims stated in reliability metrics. We then introduce a novel model-agnostic Reliability Assessment Model (RAM) for ML classifiers that utilises the operational profile and robustness verification evidence. We discuss the model assumptions and the inherent challenges of assessing ML reliability uncovered by our RAM and propose solutions to practical use. Probabilistic safety argument templates at the lower ML component-level are also developed based on the RAM. Finally, to evaluate and demonstrate our methods, we not only conduct experiments on synthetic/benchmark datasets but also scope our methods with case studies on simulated Autonomous Underwater Vehicles and physical Unmanned Ground Vehicles.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Weight Expansion: A New Perspective on Dropout and Generalization

While dropout is known to be a successful regularization technique, insights into the mechanisms that lead to this success are still lacking. We introduce the concept of \emph{weight expansion}, an increase in the signed volume of a parallelotope spanned by the column or row vectors of the weight covariance matrix, and show that weight expansion is an effective means of increasing the generalization in a PAC-Bayesian setting. We provide a theoretical argument that dropout leads to weight expansion and extensive empirical support for the correlation between dropout and weight expansion. To support our hypothesis that weight expansion can be regarded as an \emph{indicator} of the enhanced generalization capability endowed by dropout, and not just as a mere by-product, we have studied other methods that achieve weight expansion (resp.\ contraction), and found that they generally lead to an increased (resp.\ decreased) generalization ability. This suggests that dropout is an attractive regularizer, because it is a computationally cheap method for obtaining weight expansion. This insight justifies the role of dropout as a regularizer, while paving the way for identifying regularizers that promise improved generalization through weight expansion.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Abstraction and Symbolic Execution of Deep Neural Networks with Bayesian Approximation of Hidden Features

Intensive research has been conducted on the verification and validation of deep neural networks (DNNs), aiming to understand if, and how, DNNs can be applied to safety critical applications. However, existing verification and validation techniques are limited by their scalability, over both the size of the DNN and the size of the dataset. In this paper, we propose a novel abstraction method which abstracts a DNN and a dataset into a Bayesian network (BN). We make use of dimensionality reduction techniques to identify hidden features that have been learned by hidden layers of the DNN, and associate each hidden feature with a node of the BN. On this BN, we can conduct probabilistic inference to understand the behaviours of the DNN processing data. More importantly, we can derive a runtime monitoring approach to detect in operational time rare inputs and covariate shift of the input data. We can also adapt existing structural coverage-guided testing techniques (i.e., based on low-level elements of the DNN such as neurons), in order to generate test cases that better exercise hidden features. We implement and evaluate the BN abstraction technique using our DeepConcolic tool available at https://github.com/TrustAI/DeepConcolic.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Detecting Operational Adversarial Examples for Reliable Deep Learning

The utilisation of Deep Learning (DL) raises new challenges regarding its dependability in critical applications. Sound verification and validation methods are needed to assure the safe and reliable use of DL. However, state-of-the-art debug testing methods on DL that aim at detecting adversarial examples (AEs) ignore the operational profile, which statistically depicts the software's future operational use. This may lead to very modest effectiveness on improving the software's delivered reliability, as the testing budget is likely to be wasted on detecting AEs that are unrealistic or encountered very rarely in real-life operation. In this paper, we first present the novel notion of "operational AEs" which are AEs that have relatively high chance to be seen in future operation. Then an initial design of a new DL testing method to efficiently detect "operational AEs" is provided, as well as some insights on our prospective research plan.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $ω$-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy that achieves the energy-parity objective with probability $1$ when starting at a given energy level $k$, is decidable and in $NP \cap coNP$. The same holds for checking if such a $k$ exists and if a given $k$ is minimal.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Minimising Good-for-Games automata is NP complete

This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic automata, where minimality is NP-complete and PSPACE-complete, respectively. However, recent work of Radi and Kupferman has shown that minimising Co-Buchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising GFG automata might be cheaper than minimising deterministic automata. We show for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Buchi, Co-Buchi, and parity GFG automata. The proofs are a surprisingly straight forward generalisation of the proofs from deterministic Buchi automata: they use a similar reductions, and the same hard class of languages.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games

2.5 player parity games combine the challenges posed by 2.5 player reachability games and the qualitative analysis of parity games. These two types of problems are best approached with different types of algorithms: strategy improvement algorithms for 2.5 player reachability games and recursive algorithms for the qualitative analysis of parity games. We present a method that - in contrast to existing techniques - tackles both aspects with the best suited approach and works exclusively on the 2.5 player game itself. The resulting technique is powerful enough to handle games with several million states.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Incentive Stackelberg Mean-payoff Games

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader equilibria, there is a distinguished player called the leader who can assign strategies to all other players, referred to as her followers. A strategy profile is a leader strategy profile if no player, except for the leader, can improve his payoff by changing his strategy unilaterally, and a leader equilibrium is a leader strategy profile with a maximal return for the leader. In the proposed case of incentive equilibria, the leader can additionally influence the behaviour of her followers by transferring parts of her payoff to her followers. The ability to incentivise her followers provides the leader with more freedom in selecting strategy profiles, and we show that this can indeed improve the payoff for the leader in such games. The key fundamental result of the paper is the existence of incentive equilibria in mean-payoff games. We further show that the decision problem related to constructing incentive equilibria is NP-complete. On a positive note, we show that, when the number of players is fixed, the complexity of the problem falls in the same class as two-player mean-payoff games. We also present an implementation of the proposed algorithms, and discuss experimental results that demonstrate the feasibility of the analysis of medium sized games.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Lazy Probabilistic Model Checking without Determinisation

The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic Büchi automata is the inclusion of a determinisation step of the automaton under consideration. In this paper, we show that full determinisation can be avoided: subset and breakpoint constructions suffice. We have implemented our approach---both explicit and symbolic versions---in a prototype tool. Our experiments show that our prototype can compete with mature tools like PRISM.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Making the Best of Limited Memory in Multi-Player Discounted Sum Games

In this paper, we establish the existence of optimal bounded memory strategy profiles in multi-player discounted sum games. We introduce a non-deterministic approach to compute optimal strategy profiles with bounded memory. Our approach can be used to obtain optimal rewards in a setting where a powerful player selects the strategies of all players for Nash and leader equilibria, where in leader equilibria the Nash condition is waived for the strategy of this powerful player. The resulting strategy profiles are optimal for this player among all strategy profiles that respect the given memory bound, and the related decision problem is NP-complete. We also provide simple examples, which show that having more memory will improve the optimal strategy profile, and that sufficient memory to obtain optimal strategy profiles cannot be inferred from the structure of the game.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Symmetric Strategy Improvement

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of classic strategy improvement to be polynomial.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Bounded-Rate Multi-Mode Systems Based Motion Planning

Bounded-rate multi-mode systems are hybrid systems that can switch among a finite set of modes. Its dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. Given an arbitrary piecewise linear trajectory, we study the problem of following the trajectory with arbitrary precision, using motion primitives given as bounded-rate multi-mode systems. We give an algorithm to solve the problem and show that the problem is co-NP complete. We further prove that the problem can be solved in polynomial time for multi-mode systems with fixed dimension. We study the problem with dwell-time requirement and show the decidability of the problem under certain positivity restriction on the rate vectors. Finally, we show that introducing structure to the multi-mode systems leads to undecidability, even when using only a single clock variable.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Determinising Parity Automata

Parity word automata and their determinisation play an important role in automata and game theory. We discuss a determinisation procedure for nondeterministic parity automata through deterministic Rabin to deterministic parity automata. We prove that the intermediate determinisation to Rabin automata is optimal. We show that the resulting determinisation to parity automata is optimal up to a small constant. Moreover, the lower bound refers to the more liberal Streett acceptance. We thus show that determinisation to Streett would not lead to better bounds than determinisation to parity. As a side-result, this optimality extends to the determinisation of Büchi automata.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Coverage Games for Testing Nondeterministic Systems

Modern software systems may exhibit a nondeterministic behavior due to many unpredictable factors. In this work, we propose the node coverage game, a two player turn-based game played on a finite game graph, as a formalization of the problem to test such systems. Each node in the graph represents a {\em functional equivalence class} of the software under test (SUT). One player, the tester, wants to maximize the node coverage, measured by the number of nodes visited when exploring the game graphs, while his opponent, the SUT, wants to minimize it. An optimal test would maximize the cover, and it is an interesting problem to find the maximal number of nodes that the tester can guarantee to visit, irrespective of the responses of the SUT. We show that the decision problem of whether the guarantee is less than a given number is NP-complete. Then we present techniques for testing nondeterministic SUTs with existing test suites for deterministic models. Finally, we report our implementation and experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

The benefit of law-making power

We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no player has an incentive to deviate from her strategy. We argue that a player with the power to define an equilibrium is in a position, where she should not be interested in the symmetry of a Nash equilibrium, and ignore the question of whether or not her outcome can be improved if the other strategies are fixed. That is, she would only have to make sure that the other players have no incentive to deviate. This defines a greater class of equilibria, which may have better (and cannot have worse) optimal equilibria for the designated powerful player. We apply this strategy to concurrent bimatrix games and to turn based multi-player mean-payoff games. For the latter, we show that such political equilibria as well as Nash equilibria always exist, and provide simple examples where the political equilibrium is superior. We show that constructing political and Nash equilibria are NP-complete problems. We also show that, for a fixed number of players, the hardest part is to solve the underlying two-player mean-payoff games: using an MPG oracle, the problem is solvable in polynomial time. It is therefore in UP and CoUP, and can be solved in pseudo polynomial and expected subexponential time.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Time and Parallelizability Results for Parity Games with Bounded Tree and DAG Width

Parity games are a much researched class of games in NP intersect CoNP that are not known to be in P. Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small. In this paper, we study parity games on graphs with bounded treewidth, and graphs with bounded DAG width. We show that parity games with bounded DAG width can be solved in O(n^(k+3) k^(k + 2) (d + 1)^(3k + 2)) time, where n, k, and d are the size, treewidth, and number of priorities in the parity game. This is an improvement over the previous best algorithm, given by Berwanger et al., which runs in n^O(k^2) time. We also show that, if a tree decomposition is provided, then parity games with bounded treewidth can be solved in O(n k^(k + 5) (d + 1)^(3k + 5)) time. This improves over previous best algorithm, given by Obdrzalek, which runs in O(n d^(2(k+1)^2)) time. Our techniques can also be adapted to show that the problem of solving parity games with bounded treewidth lies in the complexity class NC^2, which is the class of problems that can be efficiently parallelized. This is in stark contrast to the general parity game problem, which is known to be P-hard, and thus unlikely to be contained in NC.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Bounded Satisfiability for PCTL

While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing challenge from a purely theoretical point of view, we argue that general solutions would not be of interest to practitioners: such solutions could be too big to be implementable or even infinite. Inspired by bounded synthesis techniques, we turn to the more applied problem of seeking models of a bounded size: we restrict our search to implementable -- and therefore reasonably simple -- models. We propose a procedure to decide whether or not a given PCTL formula has an implementable model by reducing it to an SMT problem. We have implemented our techniques and found that they can be applied to the practical problem of sanity checking -- a procedure that allows a system designer to check whether their formula has an unexpectedly small model.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Multiplayer Cost Games with Simple Nash Equilibria

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We study such games and show that a large class of these games, including games where the individual objectives are mean- or discounted-payoff, or quantitative reachability, and show that they do not only have a solution, but a simple solution. We establish the existence of Nash equilibria that are composed of k memoryless strategies for each agent in a setting with k agents, one main and k-1 minor strategies. The main strategy describes what happens when all agents comply, whereas the minor strategies ensure that all other agents immediately start to co-operate against the agent who first deviates from the plan. This simplicity is important, as rational agents are an idealisation. Realistically, agents have to decide on their moves with very limited resources, and complicated strategies that require exponential--or even non-elementary--implementations cannot realistically be implemented. The existence of simple strategies that we prove in this paper therefore holds a promise of implementability.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Rapid Recovery for Systems with Scarce Faults

Our goal is to achieve a high degree of fault tolerance through the control of a safety critical systems. This reduces to solving a game between a malicious environment that injects failures and a controller who tries to establish a correct behavior. We suggest a new control objective for such systems that offers a better balance between complexity and precision: we seek systems that are k-resilient. In order to be k-resilient, a system needs to be able to rapidly recover from a small number, up to k, of local faults infinitely many times, provided that blocks of up to k faults are separated by short recovery periods in which no fault occurs. k-resilience is a simple but powerful abstraction from the precise distribution of local faults, but much more refined than the traditional objective to maximize the number of local faults. We argue why we believe this to be the right level of abstraction for safety critical systems when local faults are few and far between. We show that the computational complexity of constructing optimal control with respect to resilience is low and demonstrate the feasibility through an implementation and experimental results.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Synthesis of Succinct Systems

Synthesis of correct by design systems from specification has recently attracted much attention. The theoretical results imply that this problem is highly intractable, e.g., synthesizing a system is 2EXPTIME-complete for an LTL specification, and EXPTIME-complete for a CTL specification. However, an argument against it is that the temporal specification is highly compact, and the complexity reflects the large size of the system constructed. In that respect, the complexity should, perhaps, be specified relative to the size of the minimal satisfying system. A careful observation reveals that the size of the system is presented in such arguments as the size of its state space. This view is a bit nonstandard, in the sense that the state space can be exponentially larger than the size of a reasonable implementation such as a circuit or a program. Although this alternative measure of the size of the synthesized system is more intuitive (e.g., this is the standard way model checking problems are measured), research on synthesis has so far stayed with measuring the system in terms of the explicit state space. This raises the question of whether or not there always exists a small system. In this paper, we show that this is the case if, and only if, PSPACE = EXPTIME.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Efficient Approximation of Optimal Control for Markov Games

We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately. Current techniques provide an accuracy of O(ε^2) on each interval, which leads to an infeasibly large number of intervals. We propose a sequence of approximations that achieve accuracies of O(ε^3), O(ε^4), and O(ε^5), that allow us to drastically reduce the number of intervals that are considered. For CTMDPs, the performance of the resulting algorithms is comparable to the heuristic approach given by Buckholz and Schulz, while also being theoretically justified. All of our results generalise to CTMGs, where our results yield the first practically implementable algorithms for this problem. We also provide positional strategies for both players that achieve similar error bounds.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata

In this report we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Buchi, Co-Buchi, and parity automata play a similar role in the recognition of ω-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic Buchi and parity automata has remained an open challenge. We establish the NP-completeness of these problems. A second contribution of this report is the introduction of relaxed minimisation of deterministic finite automata. Like hyper-minimisation, relaxed minimisation allows for some changes in the language of the automaton: We seek a smallest automaton that, when used as a monitor, provides a wrong answer only a bounded number of times in any run of a system. We argue that minimisation of finite automata, hyper-minimisation, relaxed minimisation, and the minimisation of deterministic Buchi (or Co-Buchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right. When we allow for minor changes in the language, relaxed minimisation can therefore be considered as a more powerful minimisation technique than hyper-minimisation from the perspective of finite automata. From the perspective of Buchi and Co-Buchi automata, we gain a cheap algorithm for state-space reduction that also turns out to be beneficial for further heuristic or exhaustive state-space reductions put on top of it.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Practical Distributed Control Synthesis

Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a single controller with complete information, resulting in a trivial control problem. But when we eliminate communication and restrict the supervisors to locally available information, the problem becomes undecidable. In this paper we argue in favor of a middle way. Communication is, in most applications, expensive, and should hence be minimized. We therefore study a solution that tries to communicate only scarcely and, while allowing communication in order to make joint decision, favors local decisions over joint decisions that require communication.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Optimal Time-Abstract Schedulers for CTMDPs and Markov Games

We study time-bounded reachability in continuous-time Markov decision processes for time-abstract scheduler classes. Such reachability problems play a paramount role in dependability analysis and the modelling of manufacturing and queueing systems. Consequently, their analysis has been studied intensively, and techniques for the approximation of optimal control are well understood. From a mathematical point of view, however, the question of approximation is secondary compared to the fundamental question whether or not optimal control exists. We demonstrate the existence of optimal schedulers for the time-abstract scheduler classes for all CTMDPs. Our proof is constructive: We show how to compute optimal time-abstract strategies with finite memory. It turns out that these optimal schedulers have an amazingly simple structure - they converge to an easy-to-compute memoryless scheduling policy after a finite number of steps. Finally, we show that our argument can easily be lifted to Markov games: We show that both players have a likewise simple optimal strategy in these more general structures.

0 citations0 reviewsNo code linkedOpen access