Automatic structures

Blumensath, Achim; Grädel, Erich

doi:10.1109/lics.2000.855755

Cited by 161 publications

(248 citation statements)

References 10 publications

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“…This extension of the binary tree is well-known as a generator of the automatic structures, in the sense that each automatic structure can be obtained from it by an FO-interpretation (cf. [BG00]). Example 2.3.…”

Section: Interpretationsmentioning

confidence: 99%

“…The extension to tree-automatic structures can be traced back, in a different framework, to the work of Dauchet and Tison [DT90]. Blumensath and Grädel [Blu99,BG00] then formalize the notion of tree-automatic structure and add to it the family of ω-tree-automatic structures. Independently, the study of 3-manyfolds lead to the particular case of automatic groups [ECH + …”

Section: Automatic-like Structuresmentioning

confidence: 99%

“…In this way, one obtains, e.g., the classes of automatic [Hod83,KN95,BG00] and tree-automatic [DT90,BG00] structures, for which the FOtheory is decidable, and the classes of pushdown-graphs [MS85] and prefix recognizable graphs [Cau96] with decidable MSO-theory. …”

Section: Introductionmentioning

confidence: 99%

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Transforming structures by set interpretations

Colcombet¹,

Löding²

2007

Logical Methods in Computer Science

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Abstract. We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.

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Section: Interpretationsmentioning

confidence: 99%

Section: Automatic-like Structuresmentioning

confidence: 99%

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Transforming structures by set interpretations

Colcombet¹,

Löding²

2007

Logical Methods in Computer Science

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“…By the properties of rational relations, the support of a rational graph is a rational subset of Γ * . The rational graphs with synchronized transducers were already defined by Blumensath and Grdel in [BG00] under the name automatic graphs and by Rispal in [Ris02] under the name synchronized rational graphs.…”

Section: Definition 22 ([Mor00])mentioning

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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“…This family lies between context-sensitive and recursively-enumerable languages in the Chomsky hierarchy. We obtain two new characterisations of ETIME, first as the languages accepted by arborescent tiling systems and second as the traces of infinite graphs defined by various classes of term transducers, namely termsynchronous and term-automatic (or tree-automatic) graphs [1].…”

Section: Introductionmentioning

confidence: 99%

Traces of Term-Automatic Graphs

Meyer

Mathematical Foundations of Computer Science 2007

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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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Automatic structures

Cited by 161 publications

References 10 publications

Transforming structures by set interpretations

Transforming structures by set interpretations

Context-Sensitive Languages, Rational Graphs and Determinism

Traces of Term-Automatic Graphs

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