Well-Structured Pushdown Systems

Cai, Xun; Ogawa, Mizuhito

doi:10.1007/978-3-642-40184-8_10

Cited by 20 publications

(14 citation statements)

References 19 publications

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“…However, among the four indexed semirings in Section 7, only the indexed semiring for conditional pushdown systems enables the decomposition above. It should be noted that Cai and Ogawa developed the forward reachability analysis of well-structured pushdown systems by combining the saturation procedure with the Karp-Miller acceleration instead of the ideal representation [CO13].…”

Section: Y Minamidementioning

confidence: 99%

Weighted Pushdown Systems with Indexed Weight Domains

Minamide¹

2016

Logical Methods in Computer Science

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Abstract. The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications.To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness.

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Section: Y Minamidementioning

confidence: 99%

Weighted Pushdown Systems with Indexed Weight Domains

Minamide¹

2016

Logical Methods in Computer Science

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“…In [2,1] the authors present decidability results for timed extensions of pushdown systems. In [14] the authors present decidability results for pushdown systems with either a well-quasi ordered set of control locations or of data values. In our model we do not consider a well-quasi ordered data domain, but introduce a well-quasi ordered relation over values pushed to and popped from the stack in order to decide reachability.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Push-Down Automata with Gap-Order Constraints

Abdulla

Atig

Delzanno

et al. 2013

Fundamentals of Software Engineering

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Abstract. We consider push-down automata with data (Pdad) that operate on variables ranging over the set of natural numbers. The conditions on variables are defined via gap-order constraint. Gap-order constraints allow to compare variables for equality, or to check that the gap between the values of two variables exceeds a given natural number. The messages inside the stack are equipped with values that are natural numbers reflecting their "values". When a message is pushed to the stack, its value may be defined by a variable in the program. When a message is popped, its value may be copied to a variable. Thus, we obtain a system that is infinite in two dimensions, namely we have a stack that may contain an unbounded number of messages each of which is equipped with a natural number. We present an algorithm for solving the control state reachability problem for Pdad based on two steps. We first provide a translation to the corresponding problem for context-free grammars with data (Cfgd). Then, we use ideas from the framework of well quasi-orderings in order to obtain an algorithm for solving the reachability problem for Cfgds.

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“…However, the semantics of this model resembles that of branching VAS [10] rather than that of a VAS with a stack. In [6], a different version of well-structured pushdown systems are introduced, which are systems where both the set of control states and the stack alphabet can be infinite and are wellquasi-ordered. They consider the coverability problem for subclasses.…”

Section: Introductionmentioning

confidence: 99%

Hyper-Ackermannian bounds for pushdown vector addition systems

Leroux

Praveen

Sutre

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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This paper studies the boundedness and termination problems for vector addition systems equipped with one stack. We introduce an algorithm, inspired by the Karp & Miller algorithm, that solves both problems for the larger class of well-structured pushdown systems. We show that the worstcase running time of this algorithm is hyper-Ackermannian for pushdown vector addition systems. For the upper bound, we introduce the notion of bad nested words over a wellquasi-ordered set, and we provide a general scheme of induction for bounding their lengths. We derive from this scheme a hyper-Ackermannian upper bound for the length of bad nested words over vectors of natural numbers. For the lower bound, we exhibit a family of pushdown vector addition systems with finite but large reachability sets (hyperAckermannian).

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Well-Structured Pushdown Systems

Cited by 20 publications

References 19 publications

Weighted Pushdown Systems with Indexed Weight Domains

Weighted Pushdown Systems with Indexed Weight Domains

Push-Down Automata with Gap-Order Constraints

Hyper-Ackermannian bounds for pushdown vector addition systems

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