Approximating Dependency Graphs Using Tree Automata Techniques

The dependency pair method of Arts and Giesl is the most powerful technique for proving termination of term rewrite systems automatically. We show that the method can be improved by using tree automata techniques to obtain better approximations of the dependency graph. This graph determines the ordering constraints that need to be solved in order to conclude termination. We further show that by using our approximations the dependency pair method provides a decision procedure for termination of right-ground rewrite systems.

[1]  Thomas Arts.  System Description: The Dependency Pair Method , 2000, RTA.

[2]  Enno Ohlebusch,et al.  Pushing the Frontiers of Combining Rewrite Systems Farther Outwards , 1998 .

[3]  Jürgen Giesl,et al.  Applying Rewriting Techniques to the Verification of Erlang Processes , 1999, CSL.

[4]  Yoshihito Toyama,et al.  Argument Filtering Transformation , 1999, PPDP.

[5]  Hans Zantema,et al.  Termination of Term Rewriting: Interpretation and Type Elimination , 1994, J. Symb. Comput..

[6]  Aart Middeldorp,et al.  Decidable Call by Need Computations in term Rewriting (Extended Abstract) , 1997, CADE.

[7]  Nachum Dershowitz.  Orderings for Term-Rewriting Systems , 1979, FOCS.

[8]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[9]  Jürgen Giesl,et al.  Termination of term rewriting using dependency pairs , 2000, Theor. Comput. Sci..

[10]  Jürgen Giesl,et al.  Eliminating Dummy Elimination , 2000, CADE.

[11]  Donald E. Knuth,et al.  Simple Word Problems in Universal Algebras††The work reported in this paper was supported in part by the U.S. Office of Naval Research. , 1970 .

[12]  Keiichirou Kusakari.  On Proving AC-Termination by AC-Dependency Paris , 1998 .

[13]  Hans Zantema,et al.  Termination of Term Rewriting by Semantic Labelling , 1995, Fundam. Informaticae.

[14]  Takashi Nagaya,et al.  Decidability for Left-Linear Growing Term Rewriting Systems , 1998, Inf. Comput..

[15]  草刈 圭一朗.  Termination, AC-Termination and dependency pairs of term rewriting systems , 2000 .

[16]  Florent Jacquemard,et al.  Decidable Approximations of Term Rewriting Systems , 1996, RTA.

[17]  Hiroyuki Seki,et al.  Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability , 2000, RTA.

[18]  Yoshihito Toyama,et al.  Decidability for Left-Linaer Growing Term Rewriting Systems , 1999, RTA.

[19]  Nachum Dershowitz.  Termination of Linear Rewriting Systems (Preliminary Version) , 1981, ICALP.

[20]  Sophie Tison.  Tree Automata and Term Rewrite Systems , 2000, RTA.

[21]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[22]  Claude Marché,et al.  Termination of Associative-Commutative Rewriting by Dependency Pairs , 1998, RTA.

[23]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[24]  Jürgen Giesl,et al.  Verification of Erlang Processes by Dependency Pairs , 2001, Applicable Algebra in Engineering, Communication and Computing.

[25]  Jürgen Giesl,et al.  Modularity of Termination Using Dependency pairs , 1998, RTA.

[26]  Hubert Comon.  Sequentiality, monadic second-order logic and tree automata , 2000 .

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

[28]  Jean-Jacques Lévy,et al.  Computations in Orthogonal Rewriting Systems, II , 1991, Computational Logic - Essays in Honor of Alan Robinson.