Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in a theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, a theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.

New results on rewrite-based satisfiability procedures

BONACINA, Maria Paola;
2009

Abstract

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in a theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, a theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.
Decision procedures; satisfiability modulo theories; combination of theories; inference; superposition; rewriting; termination; scalability
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/225588
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 71
  • ???jsp.display-item.citation.isi??? 46
social impact