A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Ciancia, Vincenzo; Sammartino, Matteo

doi:10.1007/978-3-662-45917-1_7

Cited by 5 publications

(5 citation statements)

References 41 publications

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“…Büchi RNNAs generally adhere to the paradigm of register automata, which in their original incarnation over finite words [16] are equivalent to the nominal automaton model of nondeterministic orbit-finite automata [3]. Ciancia and Sammartino [5] study deterministic nominal Muller automata accepting infinite strings of names, and show Boolean closure and decidability of inclusion. This model is incomparable to ours; details H. Urbat, D. Hausmann, S. Milius, L. Schröder XX:3 are in Section 7.…”

Section: Related Workmentioning

confidence: 99%

“…We conclude this paper by comparing Büchi RNNA with two related automata models over infinite words. Ciancia and Sammartino [5] consider deterministic nominal automata accepting data ω-languages L ⊆ A ω via a Muller acceptance condition. More precisely, a nominal deterministic Muller automaton (nDMA) A = (Q, δ, q 0 , F) is given by an orbit-finite nominal set Q of states, and equivariant map δ : Q × A → Q representing transitions, an initial state q 0 ∈ Q, and a set F ⊆ P(orb(Q)) where orb(Q) is the finite set of orbits of Q.…”

Section: Relation To Other Automata Modelsmentioning

confidence: 99%

“…Classical automata models and formal languages for finite words over finite alphabets have been extended to infinity in both directions: Infinite words model the long-term temporal development of systems, while infinite alphabets model data, such as nonces [19], object identities [14], or abstract resources [5]. We approach data ω-languages, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Nominal Büchi Automata with Name Allocation

Urbat,

Hausmann,

Milius

et al. 2021

Preprint

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Infinite words over infinite alphabets serve as models of the temporal development of the allocation and (re-)use of resources over linear time. We approach ω-languages over infinite alphabets in the setting of nominal sets, and study languages of infinite bar strings, i.e. infinite sequences of names that feature binding of fresh names; binding corresponds roughly to reading letters from input words in automata models with registers. We introduce regular nominal nondeterministic Büchi automata (Büchi RNNAs), an automata model for languages of infinite bar strings, repurposing the previously introduced RNNAs over finite bar strings. Our machines feature explicit binding (i.e. resource-allocating) transitions and process their input via a Büchi-type acceptance condition. They emerge from the abstract perspective on name binding given by the theory of nominal sets. As our main result we prove that, in contrast to most other nondeterministic automata models over infinite alphabets, language inclusion of Büchi RNNAs is decidable and in fact elementary. This makes Büchi RNNAs a suitable tool for applications in model checking.

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Section: Related Workmentioning

confidence: 99%

Section: Relation To Other Automata Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nominal Büchi Automata with Name Allocation

Urbat,

Hausmann,

Milius

et al. 2021

Preprint

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“…Nowadays, these developments are described as "nominal computation", and there is active research on its applications. Classical research questions, such as computability via Turing machines, are finding their way in this new area of computation theory [1,22], as well as algebraic description of terms with binding over richer algebraic structures than just pure names [20], coalgebraic interpretations of nominal regular expressions [23], alternative, more powerful interpretations of freshness [42,35], theories of languages of infinite words aimed at automata-theoretic model checking [9], and several other developments scattered along many research groups. This is just the surface of a much richer theory.…”

Section: Beyond Pure Namesmentioning

confidence: 99%

From urelements to Computation

Ciancia

2016

IFIP Advances in Information and Communication Technology

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Around 1922-1938, a new permutation model of set theory was defined. The permutation model served as a counterexample in the first proof of independence of the Axiom of Choice from the other axioms of Zermelo-Fraenkel set theory. Almost a century later, a model introduced as part of a proof in abstract mathematics fostered a plethora of research results, ranging from the area of syntax and semantics of programming languages to minimization algorithms and automated verification of systems. Among these results, we find Lawvere-style algebraic syntax with binders, final-coalgebra semantics with resource allocation, and minimization algorithms for mobile systems. These results are also obtained in various different ways, by describing, in terms of category theory, a number of models equivalent to the permutation model. We aim at providing both a brief history of some of these developments, and a mild introduction to the recent research line of "nominal computation theory", where the essential notion of name is declined in several different ways. Research partially funded by the European Commission FP7 ASCENS (nr. 257414), and EU QUANTICOL (nr. 600708).

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“…It is our aim in this paper to draw a similar picture for non-deterministic automata for languages over infinite alphabets. Such alphabets allow to model data, such as nonces [29], object identities [16], or abstract resources [8], and the ensuing languages are therefore called data languages. There are several species of automata for data languages in the literature.…”

Section: Introductionmentioning

confidence: 99%

Coalgebraic Semantics for Nominal Automata

Frank¹,

Milius²,

Urbat³

2022

Preprint

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This paper provides a coalgebraic approach to the language semantics of regular nominal non-deterministic automata (RNNAs), which were introduced in previous work. These automata feature ordinary as well as name binding transitions. Correspondingly, words accepted by RNNAs are strings formed by ordinary letters and name binding letters. Bar languages are sets of such words modulo α-equivalence, and to every state of an RNNA one associates its accepted bar language. We show that this semantics arises both as an instance of the Kleisli-style coalgebraic trace semantics as well as an instance of the coalgebraic language semantics obtained via generalized determinization. On the way we revisit coalgebraic trace semantics in general and give a new compact proof for the main result in that theory stating that an initial algebra for a functor yields the terminal coalgebra for the Kleisli extension of the functor. Our proof requires fewer assumptions on the functor than all previous ones. * if (1) the letter a occurs in w, and (2) the first occurrence of a is not preceded by any occurrence of a. For instance, the name a is free in a aba but not free in aaba, while the name b is free in both bar strings. This yields a natural notion of α-equivalence: Definition 2.3 (α-equivalence). Let = α be the least equivalence relation on A * such that x av = α x bw for all a, b ∈ A and x, v, w ∈ A * such that a v = b w. We denote by A * /= α the sets of α-equivalence classes of bar strings, and we write [w] α for the α-equivalence class of w ∈ A * . Remark 2.4. (1) By Pitts [37, Lem. 4.3], for every pair v, w ∈ A * the condition a v = b w holds if and only if a = b and v = w, or b # v and (a b) • v = w. (2) The equivalence relation = α is equivariant. Therefore, A * /= α forms a nominal set with the group action π • [w] α = [π • w] α for π ∈ Perm(A) and w ∈ A * .The least support of [w] α is the set of free names of w.We now compose this map with the component of ε : P ufs F → GP ufs in Remark 4.19 for X = A * /= α , and then freely extend from µF = A * /= α to P ufs (µF ) = P fs (A * /= α ) using (−) ♯ (Remark C.2). This clearly yields the desired result. ⊓ ⊔

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A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Cited by 5 publications

References 41 publications

Nominal Büchi Automata with Name Allocation

Nominal Büchi Automata with Name Allocation

From urelements to Computation

Coalgebraic Semantics for Nominal Automata

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