Rational Graphs Trace Context-Sensitive Languages

Morvan, Christophe; Stirling, Colin

doi:10.1007/3-540-44683-4_48

Cited by 17 publications

(16 citation statements)

References 11 publications

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“…This result was obtained independently of the work by Meyer showing that term-automatic infinite automata capture the class ETIME [14]. These two results, along with the characterization of NLINSPACE [15], are currently the only characterizations of complexity classes using infinite automata.…”

Section: Discussionmentioning

confidence: 79%

“…Recently, Morvan and Stirling showed the following remarkable result: infinite state automata where states are finite words, initial and final sets are defined using regular languages, and transitions are defined using rational relations, accept precisely the class of context-sensitive languages (nondeterministic linear-space languages) ( [15]; see also [5]). Rational relations are relations R ⊆ Π * × Π * that can be effected by finite-state automata: (u, u ′ ) ∈ R iff the automaton can read u on an input tape and write u ′ on the output tape, where the two tape heads are only allowed to move right (but can move independent of each other).…”

Section: Introductionmentioning

confidence: 99%

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An Infinite Automaton Characterization of Double Exponential Time

Torre

Madhusudan

Parlato

2008

Computer Science Logic

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Abstract. Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive (NLINSPACE) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETIME, the class of problems solvable in 2 2 O(n) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETIME is obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.

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Section: Discussionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

An Infinite Automaton Characterization of Double Exponential Time

Torre

Madhusudan

Parlato

2008

Computer Science Logic

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“…We give a simplified presentation of the result by Morvan and Stirling [MS01] stating that the family of rational graphs accepts the context-sensitive languages. This is done in several steps.…”

Section: The Languages Of Rational Graphsmentioning

confidence: 99%

“…with p, q, r, s ∈ Q F If we transform a rational graph into a Turing machine by applying successively the construction of Proposition 3.2, Proposition 3.7 and Theorem 2.6, we obtain the same Turing machine as in [MS01].…”

Section: Equivalence Between Synchronized Graphs and Tiling Systemsmentioning

confidence: 99%

“…The first result on this topic is due to Morvan and Stirling [MS01], who showed that the languages accepted by rational graphs, whose vertices are words and whose edges are defined by rational transducers, taken between rational or finite sets of vertices, are precisely the context-sensitive languages. This result was later extended by Rispal [Ris02] to the more restricted families of synchronized rational graphs, and even to synchronous graphs.…”

Section: Introductionmentioning

confidence: 99%

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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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Linearly Bounded Infinite Graphs

Carayol

Meyer

2005

Mathematical Foundations of Computer Science 2005

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Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions. Finally, we compare these graphs to rational graphs, which are another class of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict sub-class of linearly bounded graphs.

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Rational Graphs Trace Context-Sensitive Languages

Abstract: Abstract. This paper shows that the traces of rational graphs coincide with the context-sensitive languages.

Cited by 17 publications

References 11 publications

An Infinite Automaton Characterization of Double Exponential Time

An Infinite Automaton Characterization of Double Exponential Time

Context-Sensitive Languages, Rational Graphs and Determinism

Linearly Bounded Infinite Graphs

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