The foundations of program verification
The foundations of program verification
Theory of linear and integer programming
Theory of linear and integer programming
Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
A simple parallel algorithm for finding a satisfying truth assignment to a 2-CNF formula
Information Processing Letters
A fast and efficient parallel algorithm for finding a satisfying truth assignment to a 2-CNF formula
Information Processing Letters
An efficiently solvable graph partition problem to which many problems are reducible
Information Processing Letters
On Fourier's algorithm for linear arithmetic constraints
Journal of Automated Reasoning
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Verification of sequential and concurrent programs (2nd ed.)
Verification of sequential and concurrent programs (2nd ed.)
Artificial intelligence: a new synthesis
Artificial intelligence: a new synthesis
Deciding Linear Inequalities by Computing Loop Residues
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Proceedings of the Second International Conference on Algebraic and Logic Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
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This paper is concerned with techniques for identifying simple and quantified lattice points in 2SAT polytopes. 2SAT polytopes generalize the polyhedra corresponding to Boolean 2SAT formulae, Vertex-Packing (Covering, Partitioning) and Network flow problems; they find wide application in the domains of Program verification (Software Engineering) and State-Space search (Artificial Intelligence). Our techniques are based on the symbolic elimination strategy called the Fourier-Motzkin elimination procedure and thus have the advantages of being extremely simple (from an implementational perspective) and incremental. We also provide a characterization of the 2SAT polytope in terms of its extreme points and derive some interesting hardness results for associated optimization problems.