Semantic minimization of 3-valued propositional formulae

This paper presents an algorithm for a non-standard logic-minimization problem that arises in 3-valued propositional logic. The problem is motivated by the potential for obtaining better answers in applications that use 3-valued logic. An answer of 0 or 1 provides precise (definite) information; an answer of 1/2 provides imprecise (indefinite) information. By replacing a formula /spl phi/ with a "better" formula /spl psi/, we may improve the precision of the answers obtained. In this paper we give an algorithm that always produces a formula that is "best" (in a certain well-defined sense).

[1]  Reinhard Wilhelm,et al.  Parametric shape analysis via 3-valued logic , 2002, TOPL.

[2]  O. Coudert,et al.  A New Graph Based Prime Computation Technique , 1993 .

[3]  Shmuel Sagiv,et al.  TVLA: A System for Implementing Static Analyses , 2000, SAS.

[4]  Reinhard Wilhelm,et al.  A logic-based approach to program flow analysis , 1998, Acta Informatica.

[5]  Tsutomu Sasao,et al.  Ternary Decision Diagrams and their Applications , 1996 .

[6]  Mary Lou Soffa,et al.  Complete Removal of Redundant Computations , 1998, ACM-SIGPLAN Symposium on Programming Language Design and Implementation.

[7]  Reinhard Wilhelm,et al.  Parametric shape analysis via 3-valued logic , 1999, POPL '99.

[8]  Olivier Coudert,et al.  Two-level logic minimization: an overview , 1994, Integr..

[9]  Randal E. Bryant,et al.  Formal verification by symbolic evaluation of partially-ordered trajectories , 1995, Formal Methods Syst. Des..

[10]  B. V. Fraassen Singular Terms, Truth-Value Gaps, and Free Logic , 1966 .

[11]  S. Blamey Partial-valued logic , 1980 .

[12]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[13]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.

[14]  Willard Van Orman Quine,et al.  The Problem of Simplifying Truth Functions , 1952 .

[15]  Matthew L. Ginsberg,et al.  Multivalued logics: a uniform approach to reasoning in artificial intelligence , 1988, Comput. Intell..

[16]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[17]  Nagisa Ishiura,et al.  Shared binary decision diagram with attributed edges for efficient Boolean function manipulation , 1990, 27th ACM/IEEE Design Automation Conference.

[18]  CoudertOlivier Two-level logic minimization: an overview , 1994 .

[19]  Ching-Tsun Chou,et al.  The Mathematical Foundation fo Symbolic Trajectory Evaluation , 1999, CAV.

[20]  Delia M. Boylan Democratization and Institutional Change in Mexico , 2001 .