A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Grabmayer, Clemens; Fokkink, Wan

doi:10.48550/arxiv.2004.12740

Cited by 5 publications

(34 citation statements)

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“…The condition (W2) on a LLEE-witness C of a chart C requires the loop structure defined by C to be hierarchical. This permits to extract a star expression ẽ from C (defined in [6,7]) that expresses C in the sense that C (ẽ) ↔ C holds, intuitively by unfolding the underlying chart C to the syntax tree of ẽ. Remark 3.6.…”

Section: Definition 32 An Entry/body-labeling Of a Chartmentioning

confidence: 99%

“…Remark 3.6. In [6,7] we established a connection between charts that have a LLEE-witness (and hence satisfy LEE) and charts that are expressible by 1-free star expressions (that is, star expressions without 1, and with binary star iteration instead of unary star iteration). By saying that a chart C 'is expressible' we mean here that C is bisimilar to the chart interpretation C (ẽ) of some star expression ẽ.…”

Section: Definition 32 An Entry/body-labeling Of a Chartmentioning

confidence: 99%

“…The result of Baeten, Corradini, and myself [2] that the problem (R) is decidable in principle was based on the concept of 'well-behaved (recursive) specifications' that links process graphs with star expressions. Recently in [6,7], Wan Fokkink and I obtained a partial solution for (A) in the form of a complete proof system for '1-free' star expressions, which do not contain 1, but are formed with binary Kleene star iteration (•) ⊛ (•) instead of unary iteration. For this, we defined the 1 E.g., the process graphs C (ne) 1 and C (ne) 2 in Ex.…”

Section: Introductionmentioning

confidence: 99%

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Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

Grabmayer

2021

Electron. Proc. Theor. Comput. Sci.

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Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are finite process graphs that are not bisimilar to the process interpretation of any regular expression. For reasoning about graphs that are expressible by regular expressions it is desirable to have structural representations of process graphs in the image of the interpretation. For '1-free' regular expressions, their process interpretations satisfy the structural property LEE (loop existence and elimination). But this is not in general the case for all regular expressions, as we show by examples. Yet as a remedy, we describe the possibility to recover the property LEE for a close variant of the process interpretation. For this purpose we refine the process semantics of regular expressions to yield process graphs with 1-transitions, similar to silent moves for finite-state automata. In this section we define the process semantics of regular expressions as charts: finite labeled transition systems with initial states. We proceed by a sequence of definitions, and conclude by providing examples. Definition 2.1. We assume, for subsequent definitions implicitly, a set A whose members we call actions. The set StExp(A) of star expressions over

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Section: Definition 32 An Entry/body-labeling Of a Chartmentioning

confidence: 99%

Section: Definition 32 An Entry/body-labeling Of a Chartmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

Grabmayer

2021

Electron. Proc. Theor. Comput. Sci.

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“…pa `bq ˚"Mil ´1 `pa `bq ¨pa `bq ˚"Mil ´1 `a ¨pa `bq ˚`b ¨pa `bq The statements of Lemma 5.3, Lemma 5.4, Lemma 5.5, and Lemma 5.6 in Section 5 are adaptations to LLEE-1-charts of the statements about LLEE-charts that are expressed by Lemma 5.4, Proposition 5.5, Lemma 5.7, and Proposition 5.8 in [13,14], respectively. While the proofs of the adaptations are similar to the proofs in [13,14], we provide them here. § Lemma (= Lem.…”

Section: A2 Supplements For Sectionmentioning

confidence: 99%

“…5.2, and Ex. 5.8), but we defer proofs to the appendix due to the similarity with [13,14]. § Definition 5.1 ((relative) extraction function).…”

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A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Grabmayer

Fokkink

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

Grabmayer¹

2020

Preprint

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Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are finite process graphs that are not bisimilar to the process interpretation of any regular expression. For reasoning about graphs that are expressible by regular expressions it is desirable to have structural representations of process graphs in the image of the interpretation.For '1-free' regular expressions, their process interpretations satisfy the structural property LEE (loop existence and elimination). But this is not in general the case for all regular expressions, as we show by examples. Yet as a remedy, we describe the possibility to recover the property LEE for a close variant of the process interpretation. For this purpose we refine the process semantics of regular expressions to yield process graphs with 1-transitions, similar to silent moves for finite-state automata.This report accompanies the paper with the same title in the post-proceedings of the workshop TERMGRAPH 2020. Here we give the proofs of not only one but of both of the two central theorems. Preliminaries on the process semantics of star expressionsIn this section we define the process semantics of regular expressions as charts: finite labeled transition systems with initial states. We proceed by a sequence of definitions, and conclude by providing examples.Definition 2.1. We assume, for subsequent definitions implicitly, a set A whose members we call actions. The set StExp(A) of star expressions over

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A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Cited by 5 publications

References 10 publications

Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

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