Trace inclusion for one-counter nets revisited

Hofman, Piotr; Totzke, Patrick

doi:10.1016/j.tcs.2017.05.009

Cited by 2 publications

(1 citation statement)

References 10 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Intuitively, an OCN is a FA endowed with a nonnegative integer counter which can be incremented, decremented or left unchanged by a transition. Formally, a one-counter net [Hofman and Totzke 2018] is a tuple O = ⟨ , Σ, ⟩ where is a finite set of states, Σ is an alphabet and ⊆ × Σ × {−1, 0, 1} × is a set of transitions. A configuration of O is a pair consisting of a state ∈ and a value ∈ N for the counter.…”

Section: Inclusion In Traces Of One-counter Netsmentioning

confidence: 99%

Complete Abstractions for Checking Language Inclusion

Ganty

Ranzato

Valero

2021

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

We study the language inclusion problem L 1 ⊆ L 2 , where L 1 is regular or context-free. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of L 1 , obtained by approximating the Kleene iterates of its least fixpoint characterization, is included in L 2 . We show that a language inclusion problem is decidable whenever this overapproximating abstraction satisfies a completeness condition (i.e., its loss of precision causes no false alarm) and prevents infinite ascending chains (i.e., it guarantees termination of least fixpoint computations). This overapproximating abstraction of languages can be defined using quasiorder relations on words, where the abstraction gives the language of all the words “greater than or equal to” a given input word for that quasiorder. We put forward a range of such quasiorders that allow us to systematically design decision procedures for different language inclusion problems, such as regular languages into regular languages or into trace sets of one-counter nets, and context-free languages into regular languages. In the case of inclusion between regular languages, some of the induced inclusion checking procedures correspond to well-known state-of-the-art algorithms, like the so-called antichain algorithms. Finally, we provide an equivalent language inclusion checking algorithm based on a greatest fixpoint computation that relies on quotients of languages and, to the best of our knowledge, was not previously known.

show abstract

Section: Inclusion In Traces Of One-counter Netsmentioning

confidence: 99%

Complete Abstractions for Checking Language Inclusion

Ganty

Ranzato

Valero

2021

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

show abstract

Language Inclusion Algorithms as Complete Abstract Interpretations

2019

View full text Add to dashboard Cite

We study the language inclusion problem L1 ⊆ L2 where L1 is regular. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of L1, obtained by successively overapproximating the Kleene iterates of its least fixpoint characterization, is included in L2. We show that a language inclusion problem is decidable whenever this overapproximating abstraction satisfies a completeness condition (i.e. its loss of precision causes no false alarm) and prevents infinite ascending chains (i.e. it guarantees termination of least fixpoint computations). Such overapproximating abstraction function on languages can be defined using quasiorder relations on words where the abstraction gives the language of all words "greater than or equal to" a given input word for that quasiorder. We put forward a range of quasiorders that allow us to systematically design decision procedures for different language inclusion problems such as regular languages into regular languages or into trace sets of one-counter nets. In the case of inclusion between regular languages, some of the induced inclusion checking procedures correspond to well-known state-of-the-art algorithms like the so-called antichain algorithms. Finally, we provide an equivalent greatest fixpoint language inclusion check which relies on quotients of languages and, to the best of our knowledge, was not previously known.

show abstract

Trace inclusion for one-counter nets revisited

Cited by 2 publications

References 10 publications

Complete Abstractions for Checking Language Inclusion

Complete Abstractions for Checking Language Inclusion

Language Inclusion Algorithms as Complete Abstract Interpretations

Contact Info

Product

Resources

About