Higher Order Pushdown Automata, the Caucal Hierarchy of Graphs and Parity Games

Cachat, Thierry

doi:10.1007/3-540-45061-0_45

Cited by 42 publications

(54 citation statements)

References 12 publications

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“…For fixed points we use a trick called projection, introduced by Cachat [13]. This ingenious technique allows us to compute a fixed point of ϕ by repeatedly computing ϕ.…”

Section: Algorithm and Implementationmentioning

confidence: 99%

Analysing Mu-Calculus Properties of Pushdown Systems

Hague

Ong

2010

Model Checking Software

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Abstract. Pushdown systems provide a natural model of software with recursive procedure calls. We provide a tool implementing an algorithm for computing the winning regions of a pushdown parity game and its adaptation to the direct computation of modal µ-calculus properties over pushdown systems. We also extend the algorithm to allow backwards, as well as forwards, modalities and allow the user to restrict the control flow graph to configurations reachable from a designated initial state. These extensions are motivated by applications in dataflow analysis. We provide two sets of experimental data. First, we obtain a picture of the asymptotic behaviour by analysing random problem instances. Secondly, we use the tool to perform dataflow analysis on real-world Java programs, taken from the DaCapo benchmark suite.

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“…For fixed points we use a trick called projection, introduced by Cachat [13]. This ingenious technique allows us to compute a fixed point of ϕ by repeatedly computing ϕ.…”

Section: Algorithm and Implementationmentioning

confidence: 99%

Analysing Mu-Calculus Properties of Pushdown Systems

Hague

Ong

2010

Model Checking Software

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“…This allows one to define a complete set of runs of M on T on the grounds of a complete set of runs of − M on − R. We conclude the section with a simple example of application of Theorem 1. Let w be an infinite word over an 1 Even in the case in which t ′ is the basic − M -type of − R, we cannot guarantee the computed t to be the basic M -type of T . This further explains the need for the notions of subsumed run and complete set of runs.…”

Section: From Trees To Their Retractionsmentioning

confidence: 99%

“…Such an operation maps an A-labeled tree T to the unfolding of the rooted graph resulting from T after the addition of backwardĀ-labeled edges and #-labeled loops (cf. [1]). …”

Section: Closure Properties Of Reducible Treesmentioning

confidence: 99%

“…For a given n ∈ N, the generator G n for the n + 1-th level of the Caucal hierarchy is defined as the n-fold application of the treegraph operation to the infinite binary complete tree. These generators are closely related to another family of trees that Cachat introduces to simulate games on higher order pushdown systems [1]. These trees, denoted by C 0 , C 1 , .…”

Section: Relationships With Caucal Hierarchymentioning

confidence: 99%

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A Contraction Method to Decide MSO Theories of Deterministic Trees

Montanari

Puppis

2007

22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)

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“…Most generalizations address an extension of either of the two, or both. A rapidly growing literature is thus concerned with the case of infinite game graphs and non-regular winning conditions [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

Degrees of Lookahead in Regular Infinite Games

Holtmann

Kaiser

Thomas

2010

Foundations of Software Science and Computational Structures

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Abstract. We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent. This captures situations in distributed systems, e.g. when buffers are present in communication or when signal transmission between components is deferred. We distinguish strategies with different degrees of lookahead, among them being the continuous and the bounded lookahead strategies. In the first case the lookahead is of finite possibly unbounded size, whereas in the second case it is of bounded size. We show that for regular infinite games the solvability by continuous strategies is decidable, and that a continuous strategy can always be reduced to one of bounded lookahead. Moreover, this lookahead is at most doubly exponential in the size of the parity automaton recognizing the winning condition. We also show that the result fails for non-regular games where the winning condition is given by a context-free ω-language.

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Higher Order Pushdown Automata, the Caucal Hierarchy of Graphs and Parity Games

Cited by 42 publications

References 12 publications

Analysing Mu-Calculus Properties of Pushdown Systems

Analysing Mu-Calculus Properties of Pushdown Systems

A Contraction Method to Decide MSO Theories of Deterministic Trees

Degrees of Lookahead in Regular Infinite Games

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