Forward Regularity Preservation Property of Register Pushdown Systems

Senda, Ryoma; Takata, Yoshiaki; Seki, Hiroyuki

doi:10.1587/transinf.2020fcp0008

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…For RPDS, backward and forward regularity preservation properties were shown in [20] and [26], respectively. As a related model, register context-free grammar is also studied [9], [24], [25].…”

Section: Pds and Rpdsmentioning

confidence: 99%

LTL Model Checking for Register Pushdown Systems

Senda

Takata

Seki

2021

IEICE Trans. Inf. & Syst.

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Section: Pds and Rpdsmentioning

confidence: 99%

LTL Model Checking for Register Pushdown Systems

Senda

Takata

Seki

2021

IEICE Trans. Inf. & Syst.

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“…To extend the verification method for PDS to RPDS, the regularity preservation property of RPDS has been studied [6], [14], and recently we have proposed an LTL model checking method for RPDS with regular valuations [15]. In the model checking method in [15], we assume that a specification ϕ is given in a usual LTL formula without the ability of handling data values.…”

Section: Introductionmentioning

confidence: 99%

“…Using an LTL d ↓ formula or a system of equations in μ d ↓ -calculus, we can provide a specification ϕ that describes relations among data values in the stack tops in different IDs. Since the class of RPDS is closed under intersection with RA, we can reduce the model checking problem for RPDS and μ d ↓ -calculus specifications to the reachability problem for RPDS [6], [14]. We can also combine regular valuations with the μ d ↓ -calculus model checking, where properties inside each ID are represented by a regular valuation and properties among two or more IDs are represented by a system of equations in μ d ↓ -calculus.…”

Section: Introductionmentioning

confidence: 99%

A Subclass of Mu-Calculus with the Freeze Quantifier Equivalent to Register Automata

Takata

ONISHI

Senda

et al. 2023

IEICE Trans. Inf. & Syst.

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Register automaton (RA) is an extension of finite automaton by adding registers storing data values. RA has good properties such as the decidability of the membership and emptiness problems. Linear temporal logic with the freeze quantifier (LTL ↓ ) proposed by Demri and Lazić is a counterpart of RA. However, the expressive power of LTL ↓ is too high to be applied to automatic verification. In this paper, we propose a subclass of modal μ-calculus with the freeze quantifier, which has the same expressive power as RA. Since a conjunction ψ 1 ∧ ψ 2 in a general LTL ↓ formula cannot be simulated by RA, the proposed subclass prohibits at least one of ψ 1 and ψ 2 from containing the freeze quantifier or a temporal operator other than X (next). Since the obtained subclass of LTL ↓ does not have the ability to represent a cycle in RA, we adopt μ-calculus over the subclass of LTL ↓ , which allows recursive definition of temporal formulas. We provide equivalent translations from the proposed subclass of μ-calculus to RA and vice versa and prove their correctness.

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“…runtime verification [7] and reactive synthesis [8]. Similarly to extending FA to RA, PDS were extended to pushdown register systems (PDRS) [9] and register pushdown systems (RPDS) [10], both of them are equivalent each other, and the reachability problem for them has been shown to be EXPTIME-complete.…”

Section: Introductionmentioning

confidence: 99%

Reduction of Register Pushdown Systems with Freshness Property to Pushdown Systems in LTL Model Checking

Takata¹,

Senda²,

Seki³

2022

Preprint

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Pushdown systems (PDS) are known as an abstract model of recursive programs, and model checking methods for PDS have been studied. Register PDS (RPDS) are PDS augmented by registers to deal with data values from an infinite domain in a restricted way. A linear temporal logic (LTL) model checking method for RPDS with regular valuations has been proposed; however, the method requires the register automata (RA) used for representing a regular valuation to be backward-deterministic. This paper proposes another approach to the same problem, in which the model checking problem for RPDS is reduced to that problem for PDS by constructing a PDS bisimulation equivalent to a given RPDS. The construction in the proposed method is simpler than the previous model checking method and does not require RAs deterministic or backward-deterministic, and the bisimulation equivalence clearly guarantees the correctness of this reduction. On the other hand, the proposed method requires every RPDS (and RA) to have the freshness property, in which whenever the RPDS updates a register with a data value not stored in any register or the stack top, the value should be fresh. This paper also shows that this model checking problem with regular valuations defined by general RA is undecidable, and thus the freshness constraint is essential in the proposed method.

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Forward Regularity Preservation Property of Register Pushdown Systems

Cited by 4 publications

References 24 publications

LTL Model Checking for Register Pushdown Systems

LTL Model Checking for Register Pushdown Systems

A Subclass of Mu-Calculus with the Freeze Quantifier Equivalent to Register Automata

Reduction of Register Pushdown Systems with Freshness Property to Pushdown Systems in LTL Model Checking

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