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An efficient decision procedure for UTVPI constraints. (English) Zbl 1171.68715
Gramlich, Bernhard (ed.), Frontiers of combining systems. 5th international workshop, FroCos 2005, Vienna, Austria, September 19–21, 2005. Proceedings. Berlin: Springer (ISBN 3-540-29051-6/pbk). Lecture Notes in Computer Science 3717. Lecture Notes in Artificial Intelligence, 168-183 (2005).
Summary: A unit two variable per inequality (UTVPI) constraint is of the form $$a\cdot x + b\cdot y \leq d$$ where $$x$$ and $$y$$ are integer variables, the coefficients $$a,b \in \{-1,0,1\}$$ and the bound $$d$$ is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given $$m$$ such constraints over $$n$$ variables, the procedure checks the satisfiability of the constraints in $$O(n\cdot m)$$ time and $$O(n+m)$$ space. This improves upon the previously known $$O(n^{2}\cdot m)$$ time and $$O(n^{2})$$ space algorithm based on transitive closure. Our decision procedure is also equality generating, proof generating, and model generating.
For the entire collection see [Zbl 1089.68010].

##### MSC:
 68T15 Theorem proving (deduction, resolution, etc.) (MSC2010) 68Q25 Analysis of algorithms and problem complexity
ESC/Java
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