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# Regular expressions for infinite trees and a standard form of automata

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## Abstract

For Rabin pair automata [R1] a standard form is defined /def. 2/ i.e. such that an ordered subset {s

_{1},...,s_{2I-1}} of states is distinguished in such a way that a path of a run is accepting /rejecting if for some i even/ odd, 1≤i≤2I-1, the s_{i}appears infinitely often, and all s_{j}, j<i only finitely many times. The class of standard automata is big enough to represent all f.a. representable sets /th.1/ but has many properties similar to special automata defined in [R1]. A standard regular expression is defined /def. 6/ describing a process of forming of an infinite tree, as well as a process of building of an automaton /analysis and synthesis theorems 3,4/. The standard regular expressions are a generalisation of McNaughtons formula v d . [N] /.## Keywords

Regular Expression Finite Automaton Mixed Tree Letter Alphabet Finite Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1985