The reachability problem for ground TRS and some extensions
The reachability problem for term rewriting systems (TRS) is the problem of deciding, for a given TRS S and two terms M and N, whether M can reduce to N by applying the rules of S.
We show in this paper by some new methods based on algebraical tools of tree automata, the decidability of this problem for ground TRS's and, for every ground TRS S, we built a decision algorithm. In the order to obtain it, we compile the system S and the compiled algorithm works in a real time (as a fonction of the size of M and N).
We establish too some new results for ground TRS modulo different sets of equations : modulo commutativity of an operator σ, the reachability problem is shown decidable with technics of finite tree automata; modulo associativity, the problem is undecidable; modulo commutativity and associativity, it is decidable with complexity of reachability problem for vector addition systems.
- BRAINERS: Tree-generating regular systems, Info and control (1969)Google Scholar
- G.W. BRAMS: Reseaux de Petri:theorie et pratique,tomes 1&2, Masson, Paris (1983)Google Scholar
- CHEW: An improved algorithm for computing with equations,21st FOCS (1980)Google Scholar
- DAUCHET, HEUILLARD, LESCANNE, TISON: The confluence of ground term tewriting systems is decidable,2nd LICS (1987)Google Scholar
- DAUCHET & TISON: Tree automata and decidability in ground term rewriting systems FCT' 85 (LNCS no 199)Google Scholar
- N.DERSHOWITZ,J.HSIANG,N.JOSEPHSON and D.PLAISTED: Associative-commutative rewriting,Proc.10th IJCAI, LNCS 202 (1983)Google Scholar
- GECSEG F. & STEINBY M: tree automata,Akadémiai Kiado, Budapest (1984)Google Scholar
- HUET.G & OPPEN.D.: Equations and rewrite rules:a survey,in formal languages:perspective and open problems,Ed.Book R.,Academic Press(1980)Google Scholar
- J.P.JOUANNAUD: Church-Rosser computations with equational term rewriting systems,Proc.4th Conf on Automata, Algebra and programming,LNCS 159 (1983)Google Scholar
- C.KIRCHNER: Methodes et outils de conception systematique d'algorithmes d'unification dans les théories équationnelles,These d'etat de l'universite de Nancy I (1985)Google Scholar
- S.R.KOSARAJU: Decidability of reachability in vector addition systems, Proc.14th Ann.Symp.on Theory of Computing, 267–281.(1982)Google Scholar
- KOZEN: Complexity of finitely presented algebra, 9th ACM th. comp. (1977)Google Scholar
- E.W.MAYR: An algorithm for the general Petri net reachability problem, Siam J Comput.13 441.–460Google Scholar
- NELSON & OPPEN: Fast decision algorithms based on congruence closure, JACM 27 (1980)Google Scholar
- OYAMAGUCHI M.: The reachability problem for quasi-ground Term Rewriting Systems, Journal of Information Processing, vol 9, no4 (1986)Google Scholar
- PLAISTED D. & BACHMAIR L.: Associative path ordering, Proc. 1st conference on Rewriting Techniques and Applications, LNCS 202 (1985)Google Scholar
- RAOULT J.C.: Finiteness results on rewriting systems, RAIRO, IT, vol 15 (1985)Google Scholar