arXiv subjects

Antonín Kučera

Publications and source records attributed to Antonín Kučera.

At least 19 recordsLinked to original sources

arXiv2026

Multiagent Stochastic Shortest Path Problem

We introduce and study the multi-agent stochastic shortest path (MSSP) problem, in which $k$ agents strive to reach a target state, aiming to minimize the expected time to reach the target by any agent. We analyze the computational and strategy-complexity of the problem in both autonomous and coordinated settings, and we design efficient strategy-synthesis algorithms. The algorithms are experimentally evaluated on instances of increasing size against natural baselines.

cs.MA↗

arXiv2025

Steady-State Strategy Synthesis for Swarms of Autonomous Agents

Steady-state synthesis aims to construct a policy for a given MDP $D$ such that the long-run average frequencies of visits to the vertices of $D$ satisfy given numerical constraints. This problem is solvable in polynomial time, and memoryless policies are sufficient for approximating an arbitrary frequency vector achievable by a general (infinite-memory) policy. We study the steady-state synthesis problem for multiagent systems, where multiple autonomous agents jointly strive to achieve a suitable frequency vector. We show that the problem for multiple agents is computationally hard (PSPACE or NP hard, depending on the variant), and memoryless strategy profiles are insufficient for approximating achievable frequency vectors. Furthermore, we prove that even evaluating the frequency vector achieved by a given memoryless profile is computationally hard. This reveals a severe barrier to constructing an efficient synthesis algorithm, even for memoryless profiles. Nevertheless, we design an efficient and scalable synthesis algorithm for a subclass of full memoryless profiles, and we evaluate this algorithm on a large class of randomly generated instances. The experimental results demonstrate a significant improvement against a naive algorithm based on strategy sharing.

cs.MA↗

arXiv2025

The Satisfiability and Validity Problems for Probabilistic Computational Tree Logic are Highly Undecidable

The Probabilistic Computational Tree Logic (PCTL) is the main specification formalism for discrete probabilistic systems modeled by Markov chains. Despite serious research attempts, the decidability of PCTL satisfiability and validity problems remained unresolved for 30 years. We show that both problems are highly undecidable, i.e., beyond the arithmetical hierarchy. Consequently, there is no sound and complete deductive system for PCTL.

cs.LO↗

arXiv2024

Multiple Mean-Payoff Optimization under Local Stability Constraints

The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several mean payoffs has been deeply studied for stochastic and game-theoretic models. One common issue of the constructed controllers is the instability of the mean payoffs, measured by the deviations of the average rewards per transition computed in a finite "window" sliding along a run. Unfortunately, the problem of simultaneously optimizing the mean payoffs under local stability constraints is computationally hard, and the existing works do not provide a practically usable algorithm even for non-stochastic models such as two-player games. In this paper, we design and evaluate the first efficient and scalable solution to this problem applicable to Markov decision processes.

cs.AI↗

arXiv2024

The General and Finite Satisfiability Problems for PCTL are Undecidable

The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae.

cs.LO↗

arXiv2023

Optimizing Local Satisfaction of Long-Run Average Objectives in Markov Decision Processes

Long-run average optimization problems for Markov decision processes (MDPs) require constructing policies with optimal steady-state behavior, i.e., optimal limit frequency of visits to the states. However, such policies may suffer from local instability, i.e., the frequency of states visited in a bounded time horizon along a run differs significantly from the limit frequency. In this work, we propose an efficient algorithmic solution to this problem.

cs.MA↗

arXiv2023

Asymptotic Complexity Estimates for Probabilistic Programs and their VASS Abstractions

The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that this approach is not sufficiently robust, especially in situations when the expectations are infinite. We propose new estimates for the asymptotic analysis of probabilistic programs with non-deterministic choice that overcome this deficiency. Furthermore, we show how to efficiently compute/analyze these estimates for selected classes of programs represented as Markov decision processes over vector addition systems with states.

cs.FL↗

arXiv2023

Mean Payoff Optimization for Systems of Periodic Service and Maintenance

Consider oriented graph nodes requiring periodic visits by a service agent. The agent moves among the nodes and receives a payoff for each completed service task, depending on the time elapsed since the previous visit to a node. We consider the problem of finding a suitable schedule for the agent to maximize its long-run average payoff per time unit. We show that the problem of constructing an $\varepsilon$-optimal schedule is PSPACE-hard for every fixed $\varepsilon \geq 0$, and that there exists an optimal periodic schedule of exponential length. We propose randomized finite-memory (RFM) schedules as a compact description of the agent's strategies and design an efficient algorithm for constructing RFM schedules. Furthermore, we construct deterministic periodic schedules by sampling from RFM schedules.

cs.GT↗

arXiv2023

Synthesizing Resilient Strategies for Infinite-Horizon Objectives in Multi-Agent Systems

We consider the problem of synthesizing resilient and stochastically stable strategies for systems of cooperating agents striving to minimize the expected time between consecutive visits to selected locations in a known environment. A strategy profile is resilient if it retains its functionality even if some of the agents fail, and stochastically stable if the visiting time variance is small. We design a novel specification language for objectives involving resilience and stochastic stability, and we show how to efficiently compute strategy profiles (for both autonomous and coordinated agents) optimizing these objectives. Our experiments show that our strategy synthesis algorithm can construct highly non-trivial and efficient strategy profiles for environments with general topology.

cs.MA↗

arXiv2022

On-the-fly Adaptation of Patrolling Strategies in Changing Environments

We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender's moves and the importance of guarded targets change unpredictably. The Defender must instantly switch to a new strategy optimized for the new environment, not disrupting the ongoing patrolling task, and the new strategy must be computed promptly under all circumstances. Since strategy switching may cause unintended security risks compromising the achieved protection, our solution includes mechanisms for detecting and mitigating this problem. The efficiency of our framework is evaluated experimentally.

cs.MA↗

arXiv2022

General Optimization Framework for Recurrent Reachability Objectives

We consider the mobile robot path planning problem for a class of recurrent reachability objectives. These objectives are parameterized by the expected time needed to visit one position from another, the expected square of this time, and also the frequency of moves between two neighboring locations. We design an efficient strategy synthesis algorithm for recurrent reachability objectives and demonstrate its functionality on non-trivial instances.

cs.RO↗

arXiv2022

Minimizing Expected Intrusion Detection Time in Adversarial Patrolling

In adversarial patrolling games, a mobile Defender strives to discover intrusions at vulnerable targets initiated by an Attacker. The Attacker's utility is traditionally defined as the probability of completing an attack, possibly weighted by target costs. However, in many real-world scenarios, the actual damage caused by the Attacker depends on the \emph{time} elapsed since the attack's initiation to its detection. We introduce a formal model for such scenarios, and we show that the Defender always has an \emph{optimal} strategy achieving maximal protection. We also prove that \emph{finite-memory} Defender's strategies are sufficient for achieving protection arbitrarily close to the optimum. Then, we design an efficient \emph{strategy synthesis} algorithm based on differentiable programming and gradient descent.

cs.MA↗

arXiv2021

Deciding Polynomial Termination Complexity for VASS Programs

We show that for every fixed $k\geq 3$, the problem whether the termination/counter complexity of a given demonic VASS is $\mathcal{O}(n^k)$, $Ω(n^{k})$, and $Θ(n^{k})$ is coNP-complete, NP-complete, and DP-complete, respectively. We also classify the complexity of these problems for $k\leq 2$. This shows that the polynomial-time algorithm designed for strongly connected demonic VASS in previous works cannot be extended to the general case. Then, we prove that the same problems for VASS games are PSPACE-complete. Again, we classify the complexity also for $k\leq 2$. Interestingly, tractable subclasses of demonic VASS and VASS games are obtained by bounding certain structural parameters, which opens the way to applications in program analysis despite the presented lower complexity bounds.

cs.LO↗

arXiv2021

Regstar: Efficient Strategy Synthesis for Adversarial Patrolling Games

We design a new efficient strategy synthesis method applicable to adversarial patrolling problems on graphs with arbitrary-length edges and possibly imperfect intrusion detection. The core ingredient is an efficient algorithm for computing the value and the gradient of a function assigning to every strategy its "protection" achieved. This allows for designing an efficient strategy improvement algorithm by differentiable programming and optimization techniques. Our method is the first one applicable to real-world patrolling graphs of reasonable sizes. It outperforms the state-of-the-art strategy synthesis algorithm by a margin.

cs.GT↗

arXiv2021

The Satisfiability Problem for a Quantitative Fragment of PCTL

We give a sufficient condition under which every finite-satisfiable formula of a given PCTL fragment has a model with at most doubly exponential number of states (consequently, the finite satisfiability problem for the fragment is in 2-EXPSPACE). The condition is semantic and it is based on enforcing a form of ``progress'' in non-bottom SCCs contributing to the satisfaction of a given PCTL formula. We show that the condition is satisfied by PCTL fragments beyond the reach of existing methods.

cs.LO↗

arXiv2020

Checking Qualitative Liveness Properties of Replicated Systems with Stochastic Scheduling

We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.

cs.LO↗

arXiv2019

Deciding Fast Termination for Probabilistic VASS with Nondeterminism

A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in $Ω(n^2)$.

cs.FL↗

arXiv2018

Automatic Analysis of Expected Termination Time for Population Protocols

Population protocols are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions in which the interacting devices are chosen uniformly at random. In well designed population protocols, for every initial configuration of devices, and for every computation starting at this configuration, all devices eventually agree on a consensus value. We address the problem of automatically computing a parametric bound on the expected time the protocol needs to reach this consensus. We present the first algorithm that, when successful, outputs a function f(n) such that the expected time to consensus is bound by O(f(n)), where n is the number of devices executing the protocol. We experimentally show that our algorithm terminates and provides good bounds for many of the protocols found in the literature.

cs.LO↗