On dot-depth two
نویسندگان
چکیده
منابع مشابه
Around Dot Depth Two
It is known that the languages definable by formulae of the logics FO2[<,S], ∆2[<,S], LTL[F,P,X,Y] are exactly the variety DA∗D. Automata for this class are not known, nor is its precise placement within the dot-depth hierarchy of starfree languages. It is easy to argue that ∆2[<,S] is included in ∆3[<]; in this paper we show that it is incomparable with B(Σ2)[<], the boolean combination of Σ2[...
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Given any finite alphabet A and positive integers m1, ..., mk, congruences on A*, denoted by ~(m1, ..., mk) and related to a version of the Ehrenfeucht-Fraisse game, are defined. Level k of the Straubing hierarchy of aperiodic monoids can be characterized in terms of the monoids A*/~(m1, ... mk). A natural subhierarchy of level 2 and equation systems satisfied in the corresponding varieties of ...
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A complete set of generators for Straubing’s dot-depth-two monoids has been characterized as a set of quotients of the form A*/ wCn, , ,,, where n and M denote positive integers, A* denotes the free monoid generated by a finite alphabet A, and mCn,,,) denote congruences related to a version of the Ehrenfeucht-Frays& game. This paper studies combinatorial properties of the N~,,~)‘s and in partic...
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In this paper we pursue the study of the decidability of the dot-depth hierarchy. We give an effective lower bound for the dot-depth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal’cev product. We also prove the equality of two decidable varieties which were known to contain all dot-depth two monoids. Finally, we ...
متن کاملLanguages of Dot-Depth
We prove an effective characterization of languages having dot-depth . To our knowledge, only the classes of levels , and of the dot-depth hierarchy were known to be decidable. Let B denote the class of languages having dot-depth , i.e., languages that can be written as finite unions of languages of the form u L u L u Lnun, where ui A and Li are languages of dot-depth one. 1. Let k . We define ...
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 1990
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/1990240605211