Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Some Inference Rules for Integer Arithmetic for Verification of Flowchart Programs on Integers
IEEE Transactions on Software Engineering
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Automatic Theorem Proving With Renamable and Semantic Resolution
Journal of the ACM (JACM)
Some Completeness Results in the Mathematical Theory of Computation
Journal of the ACM (JACM)
Completeness of Linear Refutation for Theories with Equality
Journal of the ACM (JACM)
Fuzzy Logic and the Resolution Principle
Journal of the ACM (JACM)
Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets
Journal of the ACM (JACM)
An Approach for Finding C-Linear Complete Inference Systems
Journal of the ACM (JACM)
Another Generalization of Resolution
Journal of the ACM (JACM)
Experiment with an automatic theorem-prover having partial ordering inference rules
Communications of the ACM
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Deduction with Relation Matching
Proceedings of the Fifth Conference on Foundations of Software Technology and Theoretical Computer Science
Locking: A Restriction of Resolution (Dissertation), also ATP-05
Locking: A Restriction of Resolution (Dissertation), also ATP-05
Toward a man-machine system for proving program correctness
Toward a man-machine system for proving program correctness
A program verifier
A Theorem Prover for Verifying Iterative Programs Over Integers
IEEE Transactions on Software Engineering
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Because of the undecidability problem of program verification, it becomes necessary for an automated verifier to seek human assistance for proving theorems which fall beyond its capability. In order that the user be able to interact smoothly with the machine, it is desired that the theorems be maintained and processed by the prover in a form as close as possible to the popular algebraic notation. Motivated by the need of such an automated verifier, which works in an environment congenial to human participation and at the same time uses the methodologies of resolution provers of first-order logic, some inference rules have previously been proposed by the authors for integer arithmetic, and their completeness issues have been discussed. In the present work, the authors examine how these rules can be applied to quantified formulas vis-a-vis verification of programs involving arrays. An interesting situation, referred to as bound-extension, has been found to occur frequently in proving the quantified verification conditions of the paths in a program. A novel rule, called bound-extension rule, has been devised to consolidate and depict the various issues involved in a bound-extension process. It has been proved that the rule set proposed previously by the authors is adequate for handling a more general phenomenon, called bound-modification, which covers bound-extension in all its entirety.