Rewriting in the partial algebra of typed terms modulo AC

Abstract We study the partial algebra of typed terms with an associative commutative and idempotent operator (typed AC-terms). The originality lies in the representation of the typing policy by a graph which has a decidable monadic theory. In this paper we show on two examples that some results on AC-terms can be raised to the level of typed AC-terms. The examples are the results on rational languages (in particular their closure by complement) and the property reachability problem for ground rewrite systems (equivalently process rewrite systems).

[1]  Richard Mayr,et al.  Process rewrite systems , 1999, EXPRESS.

[2]  Didier Caucal,et al.  On infinite transition graphs having a decidable monadic theory , 1996, Theor. Comput. Sci..

[3]  S. Ginsburg,et al.  Semigroups, Presburger formulas, and languages. , 1966 .

[4]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs IX: Machines and their Behaviours , 1995, Theor. Comput. Sci..

[5]  David E. Muller,et al.  The Theory of Ends, Pushdown Automata, and Second-Order Logic , 1985, Theor. Comput. Sci..

[6]  Michel Hack,et al.  The Recursive Equivalence of the Reachability Problem and the Liveness Problem for Petri Nets and Vector Addition Systems , 1974, SWAT.

[7]  S. Rao Kosaraju,et al.  Decidability of reachability in vector addition systems (Preliminary Version) , 1982, STOC '82.

[8]  Philippe Schnoebelen,et al.  The regular viewpoint on PA-processes , 1998, Theor. Comput. Sci..

[9]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[10]  Sophie Tison,et al.  The theory of ground rewrite systems is decidable , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[11]  Didier Caucal.  On Infinite Terms Having a Decidable Monadic Theory , 2002, MFCS.

[12]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[13]  Pawel Urzyczyn,et al.  Higher-Order Pushdown Trees Are Easy , 2002, FoSSaCS.

[14]  Denis Lugiez,et al.  Complement Problems and Tree Automata in AC-like Theories (Extended Abstract) , 1993, STACS.