arXiv subjects

Marcin Jurdzinski

Publications and source records attributed to Marcin Jurdzinski.

9 recordsLinked to original sources

arXiv2026

Solving Streett and Emerson-Lei Games with Universal Trees

Nearly a decade ago, Calude et al. showed that parity games can be solved in quasi-polynomial time. This result is now understood in terms of universal trees. By reduction to parity games, the quasi-polymonial result can benefit all omega-regular games. However, beyond such reductions, and with the exception of Rabin games, our understanding of the role of universal trees in direct solutions is still quite limited. In this work, we refute the common view that universal trees are relevant only for games that admit memoryless winning strategies. We contribute a full understanding of how universal trees interact with Zielonka trees for the solution of Streett and Emerson-Lei games. As a consequence, we show that winning regions and strategies in Streett games with $n$ vertices, $m$ edges, and $k$ pairs can be computed in time $O(mk\log(k)k!|U(n,k)|)$, where $U(n,k)$ is a universal tree for $n$ leaves and depth $k$. This improves upon the best previously known complexity result for Streett games, which relied on reduction to parity games and their quasi-polynomial solution. Furthermore, we show that winning regions and strategies for Emerson-Lei games with $n$ vertices, $m$ edges, and $c$ colors can be computed in time $O(mc\log(c)c!|U(n,c/2)|)$, again improving over reductions to parity games. Notably, our approach yields memory-optimal strategies, in contrast to those obtained via reductions to parity games. Finally, we show how universal trees can be used to bound the recursion tree of the Zielonka-McNaughton algorithm for Emerson-Lei games. This leads to a symbolic algorithm that replaces the factor $n^c$ in the time complexity of existing symbolic approaches with $|U(n,c)|$.

cs.GT↗

arXiv2026

Fast Obligation Translation and Synthesis

Syntactic obligations are a fragment of LTL formulas that translate to deterministic weak $\omega$-automata (DWA). We show that syntactic obligations can be very efficiently converted to minimal DWA represented using multi-terminal binary decision diagrams (MTBDDs), and that synthesis of such specifications can be solved directly on the MTBDD representation on the fly. Our implementation in Spot shows substantial runtime improvements in translation and synthesis.

cs.FL↗

arXiv2018

A pseudo-quasi-polynomial algorithm for solving mean-payoff parity games

In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other player is to either foil the parity objective or to maximize the mean payoff. Our main technical result is a pseudo-quasi-polynomial algorithm for solving mean-payoff parity games. All algorithms for the problem that have been developed for over a decade have a pseudo-polynomial and an exponential factors in their running times; in the running time of our algorithm the latter is replaced with a quasi-polynomial one. By the results of Chatterjee and Doyen (2012) and of Schewe, Weinert, and Zimmermann (2018), our main technical result implies that there are pseudo-quasi-polynomial algorithms for solving parity energy games and for solving parity games with weights. Our main conceptual contributions are the definitions of strategy decompositions for both players, and a notion of progress measures for mean-payoff parity games that generalizes both parity and energy progress measures. The former provides normal forms for and succinct representations of winning strategies, and the latter enables the application to mean-payoff parity games of the order-theoretic machinery that underpins a recent quasi-polynomial algorithm for solving parity games.

cs.GT↗

arXiv2018

Succinct progress measures for solving parity games

The recent breakthrough paper by Calude et al. has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential. We devise an alternative quasi-polynomial time algorithm based on progress measures, which allows us to reduce the space required from quasi-polynomial to nearly linear. Our key technical tools are a novel concept of ordered tree coding, and a succinct tree coding result that we prove using bounded adaptive multi-counters, both of which are interesting in their own right.

cs.DS↗

arXiv2016

Mean-Payoff Games on Timed Automata

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players, Player Min and Player Max, by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.

cs.GT↗

arXiv2014

Stochastic Timed Automata

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $Φ$, we want to decide whether A satisfies $Φ$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.

cs.LO↗

arXiv2010

Alternating Automata on Data Trees and XPath Satisfiability

A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element ("datum") from an infinite set, where the latter can only be compared for equality. The article considers alternating automata on data trees that can move downward and rightward, and have one register for storing data. The main results are that nonemptiness over finite data trees is decidable but not primitive recursive, and that nonemptiness of safety automata is decidable but not elementary. The proofs use nondeterministic tree automata with faulty counters. Allowing upward moves, leftward moves, or two registers, each causes undecidability. As corollaries, decidability is obtained for two data-sensitive fragments of the XPath query language.

cs.LO↗

arXiv2009

Average-Time Games on Timed Automata

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimise the average time per transition and player Max wants to maximise it. A solution of average-time games is presented using a reduction to average-price game on a finite graph. A direct consequence is an elementary proof of determinacy for average-time games. This complements our results for reachability-time games and partially solves a problem posed by Bouyer et al., to design an algorithm for solving average-price games on priced timed automata. The paper also establishes the exact computational complexity of solving average-time games: the problem is EXPTIME-complete for timed automata with at least two clocks.

cs.GT↗

arXiv2008

Model Checking Probabilistic Timed Automata with One or Two Clocks

Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one-clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that, for one-clock probabilistic timed automata, the model-checking problem for the probabilistic timed temporal logic PCTL is EXPTIME-complete. However, the model-checking problem for the subclass of PCTL which does not permit both punctual timing bounds, which require the occurrence of an event at an exact time point, and comparisons with probability bounds other than 0 or 1, is PTIME-complete for one-clock probabilistic timed automata.

cs.LO↗