V. M. Antimirov and P. D. Mosses. Rewriting extended regular expressions. Theoretical Computer Science, 143(1):51--72, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....subalgebra. We could try to mend this discrepancy between our specification and its intended model in several ways: 1. Add further axioms to our specification, such that all ground equations involving that are satisfied in U become consequences. We have recently proved a corresponding result [1] in the absence of node construction [ and it is conjectured that the specification concerned and its correctness proof can be extended to the algebra considered here. Note that the axioms given by Kozen for his action lattices [8] relate meet only to join, not to sequencing or . ....

V. M. Antimirov and P. D. Mosses. Rewriting extended regular expressions. Technical Monograph DAIMI PB-461, Computer Science Dept., Aarhus University, 1993. A short version is to appear in Proc. Conf. on Developments in Language Theory, ed. A. Salomaa, World Scientific Publ.

....between unified algebras, which are one sorted, and many sorted algebras has been proposed in [759] where each element of a given set of sorts is viewed as a maximal element in a coalesced sum of disjoint unified algebras, each representing the constructible subsets of the appropriate sort. In [11] a novel axiomatization and rewriting theory for the unified algebra of regular events are developed, see Section 6.2. A similar approach, called equational type logic, is developed in [645, 646] In this logic, models are standard algebras equipped with a (binary) typing relation, and formulae ....

....case. There the unification procedure is tailored to handle restricted substitutivity. This work is moving gradually toward relational specifications with the syntax and reasoning systems developed on the top of the two earlier works on rewriting. 6.2. 6 Rewriting Extended Regular Expressions In [11], an extended algebra of regular events (languages) is considered, with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications, for instance in the algebraic specification ....

V. M. Antimirov and P. D. Mosses. Rewriting Extended Regular Expressions. Theoretical Computer Science, 143:51--72, 1995. \Phi.

....calculus. Finally, in Sect. 5 we review a large amount of related work, and consider possible improvements and extensions of our results. We also discuss a possible complexity A short version of this paper appeared in the Proceedings of Developments in Language Theory, Univ. of Turku, July 1993 [1]. y Current address: INRIA Lorraine CRIN, 615, rue du Jardin Botanique, B.P. 101, F 54602 Villers l es Nancy, France z BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade Bldg. 540, DK 8000 Aarhus C, Denmark 2 advantage of our approach for deciding equations between ....

....to use first (DIS ) if possible, then (SIM ) and (IND ) and (SPL) in the last turn. Still the procedure remains non deterministic: the rules can be applied to different equations in the set S. We next consider some examples to illustrate the use of TR. 2 In the short version of this paper [1] the definition of conj was not complete; here we present a corrected definition. 11 4.3 Examples The first example below is a rather simple introductory one. Examples 2 and 3 demonstrate the treatment of meet. Examples 4 and 5 show how equations involving the same extended regular expression ....

V. M. Antimirov and P. D. Mosses, Rewriting extended regular expressions (short version), in: G. Rozenberg and A. Salomaa, eds., Developments in Language Theory - At the Crossroads of Mathematics, Computer Science and Biology (World Scientific, Singapore, 1994) 195--209.

.... [9] uses derivatives to develop a procedure for proving equivalence of regular expressions; further development of this procedure is provided by Mizoguchi et al. [15] Yet another procedure for proving equivalence of extended regular expressions is suggested by the present author and Mosses [2, 3] and is also based on some constructions closely related to derivatives. In the present paper we come up with a new notion of a partial derivative which is, in a sense, a non deterministic generalization of the notion of derivative: likewise derivatives are related to DFA, partial derivatives are ....

V. M. Antimirov and P. D. Mosses. Rewriting extended regular expressions. Theoretical Comput. Sci., 141, 1995. (To appear).

.... [9] uses derivatives to develop a procedure for proving equivalence of regular expressions; further development of this procedure is provided by Mizoguchi et al. [15] Yet another procedure for proving equivalence of extended regular expressions is suggested by the present author and Mosses [2, 3] and is also based on some constructions closely related to derivatives. In the present paper we come up with a new notion of a partial derivative which is, in a sense, a non deterministic generalization of the notion of derivative: likewise derivatives are related to DFA, partial derivatives are ....

....by M. Two automata are equivalent if they recognize the same language. Regular (or rational) expressions are terms on the signature of the regular algebra Reg[A] Actually, there exist different ways to choose the signature and to formalize the algebra. In this paper we follow the idea of [2] that Reg[A] should be regarded as an order sorted algebra [10] having a sort A for an alphabet which is a subsort of a sort Reg for all the regular expressions. Here we also introduce two further subsorts of Reg, namely Reg0 and Reg1, to distinguish regular expressions denoting elements of ....

V. M. Antimirov and P. D. Mosses. Rewriting extended regular expressions (short version). In G. Rozenberg and A. Salomaa, editors, Developments in Language Theory - At the Crossroads of Mathematics, Computer Science and Biology, pages 195--209. World Scientific, Singapore, 1994.

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V. M. Antimirov and P. D. Mosses. Rewriting extended regular expressions. Theoretical Computer Science, 143(1):51--72, 1995.

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V.M. Antimirov and P.D. Mosses. Rewriting extended regular expressions. Journal of Theoretical Computer Science, 143(1):51--72, 1995.

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Antimirov, Valentin M., Mosses, Peter D. Rewriting Extended Regular Expressions. Nov 1993

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