Context-Sensitive String Languages and Recognizable Picture Languages

Latteux, Michel; Simplot, David

doi:10.1006/inco.1997.2659

Cited by 34 publications

(23 citation statements)

References 7 publications

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“…In 1990's, a robust class of "regular two dimensional languages" has been identified; it may be specified either by tile systems, or by a type of cellular automata, or by a class of monadic second-order formulas, etc. Unfortunately, the class is quite complex -for instance, emptiness property is not decidable, see [21].…”

Section: Related and Future Workmentioning

confidence: 99%

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming

Banu-Demergian

Păduraru

Ştefănescu

2013

Fundamentals of Software Engineering

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Abstract. Regular expressions and the associated regular algebra provide a rich formalism for specifying and analysing sequential models of computation. For parallel computation, extensions to handle twodimensional patterns are often required. In this paper we present a new type of regular expressions for two-dimensional patterns based on contours and their composition. Targeted applications comes from the area of modelling, specification, analysis and verification of structured interactive programs via the associated scenario semantics.

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Section: Related and Future Workmentioning

confidence: 99%

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming

Banu-Demergian

Păduraru

Ştefănescu

2013

Fundamentals of Software Engineering

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“…sets of two-dimensional words on finite alphabets [5], called local picture languages. However, by only looking at the words contained in the first row of each picture of a local picture language, one obtains a context-sensitive language, and the converse is true: for any context-sensitive language there exists a local picture language (and a tiling system accepting it) whose set of upper frontiers is that language [8].…”

Section: Arborescent Tiling Systemsmentioning

confidence: 99%

“…They were later characterised as the languages accepted by linearly space-bounded Turing machines [7], i.e. Turing machines whose runs on any input word of length n use at most k·n work tape cells, for some constant k. In [8], it was shown that context-sensitive languages also coincide with the languages accepted by bounded tiling systems.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this work is to extend the results of [8] and [4] to the more general family ETIME of languages accepted by deterministic Turing machines working in time less than 2 O(n) , or equivalently by alternating linearly bounded machines. This family lies between context-sensitive and recursively-enumerable languages in the Chomsky hierarchy.…”

Section: Introductionmentioning

confidence: 99%

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Traces of term-automatic graphs

Meyer

2008

RAIRO-Theor. Inf. Appl.

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Abstract. In formal language theory, many families of languages are defined using either grammars or finite acceptors. For instance, context-sensitive languages are the languages generated by growing grammars, or equivalently those accepted by Turing machines whose work tape's size is proportional to that of their input. A few years ago, a new characterisation of context-sensitive languages as the sets of traces, or path labels, of rational graphs (infinite graphs defined by sets of finite-state transducers) was established. We investigate a similar characterisation in the more general framework of graphs defined by term transducers. In particular, we show that the languages of term-automatic graphs between regular sets of vertices coincide with the languages accepted by alternating linearly bounded Turing machines. As a technical tool, we also introduce an arborescent variant of tiling systems, which provides yet another characterisation of these languages.Mathematics Subject Classification. 68Q45, 68Q05.

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“…Such sets of pictures are called local picture languages. However, by only looking at the words contained in the first row of each picture of a local picture language, one obtains a context-sensitive language [LS97a].…”

Section: Context Sensitive Languagesmentioning

confidence: 99%

Context-Sensitive Languages, Rational Graphs and Determinism

Carayol¹,

Meyer²

2006

Logical Methods in Computer Science

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Abstract. We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an initial vertex to a final vertex. In 2001, Morvan and Stirling proved that rational graphs accept the context-sensitive languages between rational sets of initial and final vertices. This result was later extended to sub-families of rational graphs defined by more restricted classes of transducers.Our contribution is to provide syntactical and self-contained proofs of the above results, when earlier constructions relied on a non-trivial normal form of context-sensitive grammars defined by Penttonen in the 1970's. These new proof techniques enable us to summarize and refine these results by considering several sub-families defined by restrictions on the type of transducers, the degree of the graph or the size of the set of initial vertices.

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Context-Sensitive String Languages and Recognizable Picture Languages

Cited by 34 publications

References 7 publications

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming

Traces of term-automatic graphs

Context-Sensitive Languages, Rational Graphs and Determinism

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