Automata on Infinite Objects

Thomas, Wolfgang

doi:10.1016/b978-0-444-88074-1.50009-3

Cited by 781 publications

(623 citation statements)

References 79 publications

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“…The proof is similar to the proof that MSO over words defines the same class as that of regular word languages (see [Tho90]). …”

Section: Theorem 9 (Mso Characterization) a Language L Of Nested Wordsupporting

confidence: 52%

“…The automaton A R has O(s) states. Due to complexity of complementation, B R has 2 O(s log s) states and O(s) accepting constraints [Tho90].…”

Section: Proofmentioning

confidence: 99%

“…[Tho90,VW94]). Consequently, we also define nested ω-words and consider nested word automata augmented with acceptance conditions such as Büchi and Muller, that accept languages of nested ω-words.…”

Section: Introductionmentioning

confidence: 99%

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Adding Nesting Structure to Words

Alur

Madhusudan

2006

Lecture Notes in Computer Science

147

364

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We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linear-hierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Nested words generalize both words and ordered trees, and allow both word and tree operations. We define nested word automata-finite-state acceptors for nested words, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nested word automata are as expressive as their nondeterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene-*, prefixes, and language homomorphisms; membership, emptiness, language inclusion, and language equivalence are all decidable; and definability in monadic second order logic corresponds exactly to finite-state recognizability. We also consider regular languages of infinite nested words and show that the closure properties, MSO-characterization, and decidability of decision problems carry over.The linear encodings of nested words give the class of visibly pushdown languages of words, and this class lies between balanced languages and deterministic context-free languages. We argue that for algorithmic verification of structured programs, instead of viewing the program as a context-free language over words, one should view it as a regular language of nested words (or equivalently, a visibly pushdown language), and this would allow model checking of many properties (such as stack inspection, pre-post conditions) that are not expressible in existing specification logics.We also study the relationship between ordered trees and nested words, and the corresponding automata: while the analysis complexity of nested word automata is the same as that of classical tree automata, they combine both bottom-up and top-down traversals, and enjoy expressiveness and succinctness benefits over tree automata.

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“…The proof is similar to the proof that MSO over words defines the same class as that of regular word languages (see [Tho90]). …”

Section: Theorem 9 (Mso Characterization) a Language L Of Nested Wordsupporting

confidence: 52%

“…The automaton A R has O(s) states. Due to complexity of complementation, B R has 2 O(s log s) states and O(s) accepting constraints [Tho90].…”

Section: Proofmentioning

confidence: 99%

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Adding Nesting Structure to Words

Alur

Madhusudan

2006

Lecture Notes in Computer Science

147

364

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“…WMLO is a fundamental formalism and plays an important role in automata theory; moreover, temporal logics can be translated into WMLO [20].…”

Section: Model Checking For Fragments Of Logic Of Probabilitiesmentioning

confidence: 99%

A Logic of Probability with Decidable Model-Checking

Beauquier¹,

Rabinovich

Slissenko³

2002

Computer Science Logic

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A predicate logic of probability, close to the logics of probability of Halpern et al., is introduced. Our main result concerns the following model-checking problem: deciding whether a given formula holds on the structure defined by a given finite probabilistic process. We show that this model-checking problem is decidable for a rather large subclass of formulas of a second-order monadic logic of probability. We discuss also the decidability of satisfiability and compare our logic of probability with the probabilistic temporal logic pCTL*.

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“…In MSO, quantification over set variables ranges over the subsets of N, in WMSO only over the finite subsets of N. Over labelled ω-orderings, WMSO and MSO have the same expressive power, which however exceeds that of FO[<]+MOD (cf. [17,13]). …”

Section: Logical Background and Main Resultsmentioning

confidence: 99%

Decidable Theories of the Ordering of Natural Numbers with Unary Predicates

Rabinovich

Thomas

2006

Lecture Notes in Computer Science

Self Cite

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Abstract.Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order logic. Building on the modeltheoretic composition method of Shelah, we give two characterizations of the decidable theories of this form, in terms of effectiveness conditions on two types of "homogeneous sets". We discuss the significance of these characterizations, show that the first-order theory of successor with extra predicates is not covered by this approach, and indicate how analogous results are obtained in the semigroup theoretic and the automata theoretic framework.

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Automata on Infinite Objects

Cited by 781 publications

References 79 publications

Adding Nesting Structure to Words

Adding Nesting Structure to Words

A Logic of Probability with Decidable Model-Checking

Decidable Theories of the Ordering of Natural Numbers with Unary Predicates

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