A decision procedure for term algebras with queues

In software verification it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any domain with counters, stacks, lists, and trees (but not queues) can be easily seen a special case of the term algebra, and hence a decision procedure for term algebras can be applied to decide the first-order theory of such a domain. We present a quantifier-elimination procedure for the first-order theory of term algebra extended with queues. The complete axiomatization and decidability of this theory can be immediately derived from the procedure.

[1]  Andrei Voronkov,et al.  Complexity of nonrecursive logic programs with complex values , 1998, PODS.

[2]  Kenneth Kunen,et al.  Negation in Logic Programming , 1987, J. Log. Program..

[3]  Andrei Voronkov,et al.  A decision procedure for term algebras with queues , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[4]  Hans Läuchli,et al.  Monadic second order definable relations on the binary tree , 1987, The Journal of Symbolic Logic.

[5]  Wilfrid Hodges,et al.  Model Theory: The existential case , 1993 .

[6]  J. Ferrante,et al.  The computational complexity of logical theories , 1979 .

[7]  C. Ward Henson,et al.  A Uniform Method for Proving Lower Bounds on the Computational Complexity of Logical Theories , 1990, Ann. Pure Appl. Log..

[8]  Hugo Volger.  Turing Machines with Linear Alternation, Theories of Bounded Concatenation and the Decision Problem of First Order Theories , 1983, Theor. Comput. Sci..

[9]  Z. Manna,et al.  Integrating decision procedures for temporal verification , 1998 .

[10]  Howard Barringer,et al.  Efficient CTL* model checking for analysis of rainbow designs , 1997, CHARME.

[11]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[12]  A. I. Malcev.  Axiomatizable classes of locally free algebras of various types , 1971 .

[13]  Jean-Pierre Jouannaud,et al.  Syntacticness, Cycle-Syntacticness, and Shallow Theories , 1994, Inf. Comput..

[14]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[15]  Michael J. Maher.  Complete axiomatizations of the algebras of finite, rational and infinite trees , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[16]  Hubert Comon-Lundh,et al.  Equational Problems and Disunification , 1989, J. Symb. Comput..

[17]  Nicolas Peltier.  Increasing Model Building Capabilities by Constraint Solving on Terms with Integer Exponents , 1997, J. Symb. Comput..

[18]  Iu I Khmelevskiĭ.  Equations in free semigroups , 1976 .