: PIN J.-E., Logic, semigroups and automata on words, to appear in Annals of Mathematics and Articial Intelligence.  Home/Search   Document Not in Database   Summary   Related Articles

.... the structures representing the words of ab c among those of STR(Rw;A ) The languages characterized in this way by a rst order formula form a subclass of the class of regular languages, called the class of locally threshold testable languages (see Thomas [63] or the survey by Pin [52]) 4 1.3 Second order logic We now let X contain individual variables as in Subsection 1.2 and also relation variables, denoted by uppercase letters, X;Y; X 1 ; Xn . Each relation variable has an arity which is a positive integer ( X) is the arity of X) We let R be a nite set of ....

....the strictness of the corresponding hierarchy of graph properties, relativized to various classes of graphs or related objects like words, partial orders and hypergraphs. The languages de ned by monadic second order formulas are the regular languages by a theorem of [8] see also the survey by Pin [52]) 1.5 Decidability questions Let R be a nite set of relation symbols. Let L be a class of closed formulas expressing properties of the structures in STR(R) Let C STR(R) The L theory of C is the set : ThL (C) f 2 L=S j= for every S 2 Cg: We say that the L theory of C is decidable if ....

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: PIN J.-E., Logic, semigroups and automata on words, to appear in Annals of Mathematics and Articial Intelligence.

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