Formats of Winning Strategies for Six Types of Pushdown Games

  title={Formats of Winning Strategies for Six Types of Pushdown Games},
  author={Wladimir Fridman},
  booktitle={International Symposium on Games, Automata, Logics and Formal Verification},
  • Wladimir Fridman
  • Published in
    International Symposium on…
    7 June 2010
  • Computer Science
The solution of parity games over pushdown graphs (Walukiewicz ’96) was the first step towards an effective theory of infinite-state games. It was shown that w inning strategies for pushdown games can be implemented again as pushdown automata. We continue this study and investigate the connection between game presentations and winning strategies in altogether six cases of game arenas, among them realtime pushdown systems, visibly pushdown systems, and counter systems. In four cases we show by a… 

Figures from this paper

Languages and strategies: a study of regular infinite games

The fundamental Büchi-Landweber Theorem is extended and refine to subclasses of the class of regular languages, in particular the authors consider hierarchies below the starfree languages and distinguish between weak games and strong games.

Optimal Strategies in Pushdown Reachability Games

An algorithm for computing optimal strategies in pushdown reachability games is shown to be too coarse and the strategies constructed are not necessarily optimal, but the algorithm can be refined to recover optimality.

Synthesis of winning strategies for interaction under partial information

This work adresses the strategy problem for multiplayer games with imperfect information which are of infinite duration and have (up to) contextfree winning conditions and provides a complete characterization of all communication graphs for which synthesis is decidable for locally decomposable regular and contextfree specifications.

Good-for-games ω-Pushdown Automata

These are automata whose nondeterminism can be resolved based on the run constructed thus far and it follows that the universality problem for ω-GFG-PDA is in EXPTIME as well.

Decision Problems for Deterministic Pushdown Automata on Infinite Words

Some decidability results on variations of the basic simplification question asks whether one can determine the minimal number of priorities that are needed to accept the language of a given omega-DPDA for some classes of omega-DPDAs are provided.

Simplification problems for automata and games

This thesis continues the research on two aspects of simplications, namely regularity problems and lookahead delegation and shows the regularity problem to be undecidable even for PDGs with safety acceptance.

Simplification Problems for Deterministic Pushdown Automata on Infinite Words

Some decidability results concerning simplification problems for DPDAs on infinite words (ω-DPDAs) are surveyed and some insights are given on the equivalence problem for a subclass of ω-DPDA.

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

It is proved that HD-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL) and this class is orthogonal to unambiguous CFL.

Infinite Games and Uniformization

The problem of solvability of infinite games is closely connected with the classical question of uniformization of relations by functions of a given class and recent results on infinite games that are motivated by the uniformization problem are discussed.



Two-Way Tree Automata Solving Pushdown Games

  • Thierry Cachat
  • Computer Science
    Automata, Logics, and Infinite Games
  • 2001
This paper studies parity games on a simple class of infinite graphs: the pushdown (transition) graphs and presents a generalization of the (one-way) tree automata presented in Chapters 8 and 9.

Visibly Pushdown Games

The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems and it is established that, unlike pushdown games with pushdown winning conditions, visibly push down games are decidable and are 2Exptime-complete.

Pushdown Processes: Games and Model-Checking

It is shown that the model checking problem for push-down automata and the propositional μ-calculus is DEXPTIME-complete and there is a winning strategy which is realized by a pushdown process.

Solving sequential conditions by finite-state strategies

Our main purpose is to present an algorithm which decides whether or not a condition 𝕮(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This

Visibly pushdown languages

This framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures withrespect to pre and post conditions.

Logical Refinements of Church's Problem

This work presents several logics L such that Church's Problem with respect to L has also a solution in L, and discusses some perspectives of this approach.

Tree Automata, Mu-Calculus and Determinacy (Extended Abstract)

The propositional Mu-Calculus is equivalent in expressive power to finite automata on infinite trees and provides a radically simplified, alternative proof of Rabin's complementation lemma for tree automata, which is the heart of one of the deepest decidability results.

Reasoning about The Past with Two-Way Automata

The main result in this paper is an exponential time upper bound for the satisfiability problem of the Μ-calculus with both forward and backward modalities, developed a theory of two-way alternating automata on infinite trees.

An Automata-Theoretic Approach to Reasoning about Infinite-State Systems

An automata-theoretic framework for reasoning about infinite-state sequential systems based on the observation that states of such systems can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata.

Logic, arithmetic, and automata

This paper is a summary of recent work in the application of mathematical logic to finite automata, and especially of Mathematical logic beyond propositional calculus to autom-ata theory, in which the context is biological.