F.Bossut, M.Dauchet, B.Warin; A Kleene theorem for a class of planar acyclic graphs, Inform. and Comput. 117 (1995), 251-265  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... nets, form the basis of the theory of x categories developed in [Hot1] also called strict monoidal categories, see, e.g. EhrKKK, Ben] Free x categories model the sets of derivation graphs of Chomsky type 0 grammars (see [Hot2, Ben] Finite automata on such graphs are considered, e.g. in [BosDW]. The idea of using concatenation and sum in graph grammars is from [HotKM] where logic topological nets are generated by graph grammars (with parallel rewriting) Our first main result (mentioned above) confirms the naturalness of these operations. Our main interest in this paper is in the ....

F.Bossut, M.Dauchet, B.Warin; A Kleene theorem for a class of planar acyclic graphs, Inform. and Comput. 117 (1995), 251-265

....a precise description of the class of acyclic graphs where in graph acceptors the use of 1 sphere transitions suffices. It seems that planarity conditions are useful in this context (as they occur also in the set up of regular expressions for describing languages of labelled acyclic graphs, cf. [BDW95]) Let us turn to the occurrence constraints. In the next proposition we use graphs Gn which are made up of vertices u 1 ; un and v 1 ; v n as follows: From u i there are two edges, one to v i (labelled 0) and one to v ( i 1) mod n) labelled 1) Imagine the u i and the v i ....

....of work which have not been touched in this paper and which deserve more study. Already in the introduction we mentioned the subject of monadic second order properties of infinite partial orders. Another track is the description of properties by calculi of regular expressions (as pursued in [BDW95]) or by algebraic notions of recognizability (as developed in Courcelle s work [Cou90] Cou96] Finally, for applications in decision problems of logic or in program verification the complexity of the transformation procedures from logical formulas to finite state acceptors need to be analyzed. ....

F. Bossut, M. Dauchet, B. Warin, A Kleene Theorem for a class of planar acyclic graphs, Inform. and Comput. 117 (1995), 251-265.

.... nets, form the basis of the theory of x categories developed in [Hot1] also called strict monoidal categories, see, e.g. EhrKKK, Ben] Free x categories model the sets of derivation graphs of Chomsky type 0 grammars (see [Hot2, Ben] Finite automata on such graphs are considered, e.g. in [BosDW]. The idea of using concatenation and sum in graph grammars is from [HotKM] where logic topological nets are generated by graph grammars (with parallel rewriting) Our first main result (mentioned above) confirms the naturalness of these operations. Our main interest in this paper is in the ....

F.Bossut, M.Dauchet, B.Warin; A Kleene theorem for a class of planar acyclic graphs, Inform. and Comput. 117 (1995), 251-265

....descriptive formalisms. Instead of systems of classical logic, more restrictive systems should be studied, whose expressive power might suffice for interesting applications but with acceptable complexity bounds e.g. for the satisfiability problem. These can be versions of regular expressions (cf. [BDW95]) or restrictions of EMSO logic, or of FO[ logic, over partial orders. 4) Comparison with the algebraic approach to recognizability. Here we refer to Courcelle s theory of recognizability, which is based on many sorted and locally finite graph algebras (cf. Cou90] The class of recognizable ....

F. Bossut, M. Dauchet, B. Warin, A Kleene Theorem for a class of planar acyclic graphs, Inform. and Comput. 117 (1995), 251-265.

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: BOSSUT F., DAUCHET M., WARIN B., A Kleene theorem for a class of planar acyclic graphs, Information and Computation 117 (1995) 251-265.

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