arXiv subjects

Ocan Sankur

Publications and source records attributed to Ocan Sankur.

At least 19 recordsLinked to original sources

arXiv2025

On Dynamic Programming Theory for Leader-Follower Stochastic Games

Leader-follower general-sum stochastic games (LF-GSSGs) model sequential decision-making under asymmetric commitment, where a leader commits to a policy and a follower best responds, yielding a strong Stackelberg equilibrium (SSE) with leader-favourable tie-breaking. This paper introduces a dynamic programming (DP) framework that applies Bellman recursion over credible sets-state abstractions formally representing all rational follower best responses under partial leader commitments-to compute SSEs. We first prove that any LF-GSSG admits a lossless reduction to a Markov decision process (MDP) over credible sets. We further establish that synthesising an optimal memoryless deterministic leader policy is NP-hard, motivating the development of {\epsilon}-optimal DP algorithms with provable guarantees on leader exploitability. Experiments on standard mixed-motive benchmarks-including security games, resource allocation, and adversarial planning-demonstrate empirical gains in leader value and runtime scalability over state-of-the-art methods.

cs.GT↗

arXiv2025

Linear Planar 3-SAT and Its Applications in Planning

Several fragments of the satisfiability problem have been studied in the literature. Among these, Linear 3-SAT is a satisfaction problem in which each clause (viewed as a set of literals) intersects with at most one other clause; moreover, any pair of clauses have at most one literal in common. Planar 3-SAT is a fragment which requires that the so-called variable-clause graph is planar. Both fragments are NP-complete and have applications in encoding NP-hard planning problems. In this paper, we investigate the complexity and applications of the fragment obtained combining both features. We define Linear Planar 3-SAT and prove its NP-completeness. We also study the reconfiguration problem of Linear Planar 3-SAT and show that it is PSPACE-complete. As an application, we use these new results to prove the NP-completeness of Bounded Connected Multi-Agent Pathfinding and the PSPACE-completeness of Connected Multi-Agent Pathfinding in two-dimensional grids.

cs.CC↗

arXiv2025

The Value Problem for Multiple-Environment MDPs with Parity Objective

We consider multiple-environment Markov decision processes (MEMDP), which consist of a finite set of MDPs over the same state space, representing different scenarios of transition structure and probability. The value of a strategy is the probability to satisfy the objective, here a parity objective, in the worst-case scenario, and the value of an MEMDP is the supremum of the values achievable by a strategy. We show that deciding whether the value is 1 is a PSPACE-complete problem, and even in P when the number of environments is fixed, along with new insights to the almost-sure winning problem, which is to decide if there exists a strategy with value 1. Pure strategies are sufficient for theses problems, whereas randomization is necessary in general when the value is smaller than 1. We present an algorithm to approximate the value, running in double exponential space. Our results are in contrast to the related model of partially-observable MDPs where all these problems are known to be undecidable.

cs.LO↗

arXiv2024

Parameterized Verification of Timed Networks with Clock Invariants

We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via location guards that enable a transition only if there is another process in a certain location. We solve for the first time the case with unrestricted clock invariants, and establish that the parameterized model checking problem (PMCP) over finite local traces can be reduced to the corresponding model checking problem on a single TA. Moreover, we prove that the PMCP for networks that communicate via lossy broadcast can be reduced to the PMCP for DTNs. Finally, we show that for networks with k-wise synchronization, and therefore also for timed Petri nets, location reachability can be reduced to location reachability in DTNs. As a consequence we can answer positively the open problem from Abdulla et al.(2018) whether the universal safety problem for timed Petri nets with multiple clocks is decidable.

cs.FL↗

arXiv2024

Online Test Synthesis From Requirements: Enhancing Reinforcement Learning with Game Theory

We consider the automatic online synthesis of black-box test cases from functional requirements specified as automata for reactive implementations. The goal of the tester is to reach some given state, so as to satisfy a coverage criterion, while monitoring the violation of the requirements. We develop an approach based on Monte Carlo Tree Search, which is a classical technique in reinforcement learning for efficiently selecting promising inputs. Seeing the automata requirements as a game between the implementation and the tester, we develop a heuristic by biasing the search towards inputs that are promising in this game. We experimentally show that our heuristic accelerates the convergence of the Monte Carlo Tree Search algorithm, thus improving the performance of testing.

cs.AI↗

arXiv2023

Games on Graphs: From Logic and Automata to Algorithms

The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became important for program verification and synthesis. They have many more applications, in particular some of the models investigated in this book were introduced and studied in neighbouring research communities such as optimisation, reinforcement learning, model theory, and set theory.

cs.GT↗

arXiv2022

Zone-based verification of timed automata: extrapolations, simulations and what next?

Timed automata have been introduced by Rajeev Alur and David Dill in the early 90's. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on the traversal of their state-space using zones as a symbolic representation. Since the state-space is infinite, termination relies on finite abstractions that yield a finite representation of the reachable states. The first solution to get finite abstractions was based on extrapolations of zones, and has been implemented in the industry-strength tool Uppaal. A different approach based on simulations between zones has emerged in the last ten years, and has been implemented in the fully open source tool TChecker. The simulation-based approach has led to new efficient algorithms for reachability and liveness in timed automata, and has also been extended to richer models like weighted timed automata, and timed automata with diagonal constraints and updates. In this article, we survey the extrapolation and simulation techniques, and discuss some open challenges for the future.

cs.LO↗

arXiv2022

Non-Blind Strategies in Timed Network Congestion Games

Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using the same link. Network congestion games have been extensively studied over the last 40 years, while their extension with timing constraints were considered more recently. Most of the results on network congestion games consider blind strategies: they are static, and do not adapt to the strategies selected by the other players. We extend the recent results of [Bertrand et al., Dynamic network congestion games. FSTTCS'20] to timed network congestion games, in which the availability of the edges depend on (discrete) time. We prove that computing Nash equilibria satisfying some constraint on the total cost (and in particular, computing the best and worst Nash equilibria), and computing the social optimum, can be achieved in exponential space. The social optimum can be computed in polynomial space if all players have the same source and target.

cs.GT↗

arXiv2022

Parameterized safety verification of round-based shared-memory systems

We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm [J. Aspnes, Fast deterministic consensus in a noisy environment. Journal of Algorithms, 2002], we consider round-based distributed algorithms communicating with shared memory. A particular challenge in these systems is that 1) the number of processes is unbounded, and, more importantly, 2) there is a fresh set of registers at each round. A~verification algorithm thus needs to manage both sources of infinity. In this setting, we prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For~negative instances of the safety verification problem, we~also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered.

cs.FL↗

arXiv2022

The variance-penalized stochastic shortest path problem

The stochastic shortest path problem (SSPP) asks to resolve the non-deterministic choices in a Markov decision process (MDP) such that the expected accumulated weight before reaching a target state is maximized. This paper addresses the optimization of the variance-penalized expectation (VPE) of the accumulated weight, which is a variant of the SSPP in which a multiple of the variance of accumulated weights is incurred as a penalty. It is shown that the optimal VPE in MDPs with non-negative weights as well as an optimal deterministic finite-memory scheduler can be computed in exponential space. The threshold problem whether the maximal VPE exceeds a given rational is shown to be EXPTIME-hard and to lie in NEXPTIME. Furthermore, a result of interest in its own right obtained on the way is that a variance-minimal scheduler among all expectation-optimal schedulers can be computed in polynomial time.

math.OC↗

arXiv2020

Dynamic network congestion games

Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the resources correspond to simple paths in a graph, e.g. representing routing options from a source to a target. In this paper, we introduce a variant of NCGs, referred to as dynamic NCGs: in this setting, players take transitions synchronously, they select their next transitions dynamically, and they are charged a cost that depends on the number of players simultaneously using the same transition. We study, from a complexity perspective, standard concepts of game theory in dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria. Our contributions are the following: the existence of a strategy profile with social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium with bounded cost can be decided in EXPSPACE, and computing a witnessing strategy profile can be done in doubly-exponential time. The existence of a subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and a witnessing strategy profile can be computed in triply-exponential time.

cs.GT↗

arXiv2020

Incremental methods for checking real-time consistency

Requirements engineering is a key phase in the development process. Ensuring that requirements are consistent is essential so that they do not conflict and admit implementations. We consider the formal verification of rt-consistency, which imposes that the inevitability of definitive errors of a requirement should be anticipated, and that of partial consistency, which was recently introduced as a more effective check. We generalize and formalize both notions for discrete-time timed automata, develop three incremental algorithms, and present experimental results.

cs.FL↗

arXiv2020

Conflict-Based Search for Connected Multi-Agent Path Finding

We study a variant of the multi-agent path finding problem (MAPF) in which agents are required to remain connected to each other and to a designated base. This problem has applications in search and rescue missions where the entire execution must be monitored by a human operator. We re-visit the conflict-based search algorithm known for MAPF, and define a variant where conflicts arise from disconnections rather than collisions. We study optimizations, and give experimental results in which we compare our algorithms with the literature.

cs.AI↗

arXiv2019

Abstraction Refinement Algorithms for Timed Automata

We present abstraction-refinement algorithms for model checking safety properties of timed automata. The abstraction domain we consider abstracts away zones by restricting the set of clock constraints that can be used to define them, while the refinement procedure computes the set of constraints that must be taken into consideration in the abstraction so as to exclude a given spurious counterexample. We implement this idea in two ways: an enumerative algorithm where a lazy abstraction approach is adopted, meaning that possibly different abstract domains are assigned to each exploration node; and a symbolic algorithm where the abstract transition system is encoded with Boolean formulas.

cs.FL↗

arXiv2019

Reachability and Coverage Planning for Connected Agents: Extended Version

Motivated by the increasing appeal of robots in information-gathering missions, we study multi-agent path planning problems in which the agents must remain interconnected. We model an area by a topological graph specifying the movement and the connectivity constraints of the agents. We study the theoretical complexity of the reachability and the coverage problems of a fleet of connected agents on various classes of topological graphs. We establish the complexity of these problems on known classes, and introduce a new class called sight-moveable graphs which admit efficient algorithms.

cs.AI↗

arXiv2018

Stochastic Shortest Paths and Weight-Bounded Properties in Markov Decision Processes

The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the accumulated weights. These algorithms are used to provide solutions for two types of fundamental problems for integer-weighted MDPs. First, a polynomial-time algorithm for the classical stochastic shortest path problem is presented, generalizing known results for special classes of weighted MDPs. Second, qualitative probability constraints for weight-bounded (repeated) reachability conditions are addressed. Among others, it is shown that the problem to decide whether a disjunction of weight-bounded reachability conditions holds almost surely under some scheduler belongs to $\textrm{NP}\cap \textrm{coNP}$, is solvable in pseudo-polynomial time and is at least as hard as solving two-player mean-payoff games, while the corresponding problem for universal quantification over schedulers is solvable in polynomial time.

cs.LO↗

arXiv2017

The 4th Reactive Synthesis Competition (SYNTCOMP 2017): Benchmarks, Participants & Results

We report on the fourth reactive synthesis competition (SYNTCOMP 2017). We introduce two new benchmark classes that have been added to the SYNTCOMP library, and briefly describe the benchmark selection, evaluation scheme and the experimental setup of SYNTCOMP 2017. We present the participants of SYNTCOMP 2017, with a focus on changes with respect to the previous years and on the two completely new tools that have entered the competition. Finally, we present and analyze the results of our experimental evaluation, including a ranking of tools with respect to quantity and quality of solutions.

cs.LO↗

arXiv2017

Admissibility in Concurrent Games

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates it, i.e., that wins (almost surely) against a super set of adversarial strategies. We prove that admissible strategies always exist in concurrent games, and we characterise them precisely. Then, when the objectives of the players are omega-regular, we show how to perform assume-admissible synthesis, i.e., how to compute admissible strategies that win (almost surely) under the hypothesis that the other players play admissible

cs.GT↗