Two-Way Tree Automata Solving Pushdown Games

Cachat, Thierry

doi:10.1007/3-540-36387-4_17

Cited by 12 publications

(19 citation statements)

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“…The main idea was to reduce a model-checking problem to an emptiness problem for a class of tree automata, namely alternating two-way parity tree automata. This technique can then be adapted to solve parity pushdown games [4].…”

Section: Upper Boundmentioning

confidence: 99%

“…Let us first informally recall the construction of [4], and explain how to simplify it in the special case of one-counter parity games. It is rather standard to consider that the complete infinite tree of arity k is a representation of the set of all finite words on an alphabet of cardinality k. Each node in this tree is labeled by the last letter of the word it represents: hence the word associated to some node is obtained by considering the sequence of labels of the nodes on the path from the root to the current one.…”

Section: Upper Boundmentioning

confidence: 99%

“…We consider parity games played on one-counter graphs and provide a PSpace algorithm to decide the winner in such games. Our procedure relies on a tricky adaptation and a precise analysis of the techniques from [11,4] that were originally developed for pushdown games. Our result improves the ExpTime upper bound inherited from pushdown games [22].…”

Section: Introductionmentioning

confidence: 99%

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Parity Games Played on Transition Graphs of One-Counter Processes

Serre

2006

Lecture Notes in Computer Science

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We consider parity games played on special pushdown graphs, namely those generated by one-counter processes. For parity games on pushdown graphs, it is known from [22] that deciding the winner is an ExpTime-complete problem. An important corollary of this result is that the µ-calculus model checking problem for pushdown processes is Exp-Time-complete. As one-counter processes are special cases of pushdown processes, it follows that deciding the winner in a parity game played on the transition graph of a one-counter process can be achieved in Ex-pTime. Nevertheless the proof for the ExpTime-hardness lower bound of [22] cannot be adapted to that case. Therefore, a natural question is whether the ExpTime upper bound can be improved in this special case. In this paper, we adapt techniques from [11, 4] and provide a PSpace upper bound and a DP-hard lower bound for this problem. We also give two important consequences of this result. First, we improve the best upper bound known for model-checking one-counter processes against µ-calculus. Second, we show how these games can be used to solve pushdown games with winning conditions that are Boolean combinations of a parity condition on the control states with conditions on the stack height.

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Section: Upper Boundmentioning

confidence: 99%

Section: Upper Boundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parity Games Played on Transition Graphs of One-Counter Processes

Serre

2006

Lecture Notes in Computer Science

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“…The leaves of the run may be labeled by states of a strictly lower stratum or negations thereof, or by states of the same stratum whose transition function is tautological, i.e., by some (q , w) such that ∆(q , λ(w)) has ∅, ∅ as a satisfying assignment. Intuitively, if we disallow negation in transitions, our automata amount to the alternating two-way automata used by [22], with the simplification that they do not need parity acceptance conditions (because we only work with finite trees), and that they are isotropic: the run for each positive child state of an internal node may start indifferently on any neighbor of w in the tree (its parent, a child, or w itself), no matter the direction. (Note, however, that the run for negated child states must start on w itself.…”

Section: Translation To Automatamentioning

confidence: 99%

Evaluating Datalog via Tree Automata and Cycluits

et al. 2019

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We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.

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“…For the proof see [3]. Note that since T stack is the only tree which can be accepted by B, it holds that T stack ∈ L(B) if and only if L(B) = / 0.…”

Section: A2ta Simulating a Pushdown Game Letmentioning

confidence: 99%

Formats of Winning Strategies for Six Types of Pushdown Games

Fridman

2010

Electron. Proc. Theor. Comput. Sci.

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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 winning 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 uniform proof method that we obtain strategies implementable by the same type of pushdown machine as given in the game arena. We prove that for the two remaining cases this correspondence fails. In the conclusion we address the question of an abstract criterion that explains the results

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Two-Way Tree Automata Solving Pushdown Games

Cited by 12 publications

References 0 publications

Parity Games Played on Transition Graphs of One-Counter Processes

Parity Games Played on Transition Graphs of One-Counter Processes

Evaluating Datalog via Tree Automata and Cycluits

Formats of Winning Strategies for Six Types of Pushdown Games

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