Related papers: The 2-Token Theorem: Recognising History-Determini…

Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems. First, it was known that there is a family of unary promise problems solvable by quantum automata…

We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the…

We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for…

A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…

We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider…

In a reachability-time game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachability-time games on strongly…

Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…

We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor…

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two…

Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…

In 1998 Zielonka simplified the proofs of memoryless determinacy of infinite parity games. In 2018 Haddad simplified some proofs of memoryless determinacy of finite parity games. This article adapts Haddad's technique for infinite parity…

We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…

In a two-player zero-sum graph game, the players move a token throughout a graph to produce an infinite play, which determines the winner of the game. Bidding games are graph games in which in each turn, an auction (bidding) determines…

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…

A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…

Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently…

The parity index problem of tree automata asks, given a regular tree language L, what is the least number of priorities of a nondeterministic parity tree automaton that recognises L. This is a long-standing open problem, also known as the…

The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…

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…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…