From Satisfiability to Linear Algebra
نویسنده
چکیده
Satisfiability of boolean formulas (SAT) is an interesting problem for many reasons. It was the first problem proved to be NP-complete by Cook. Efficient SAT solvers have many applications. In fact, there is a huge literature on SAT, and its connections with other optimization problems have been explored. In this paper, we look at SAT using linear algebra, a basic and fundamental mathematics that have mature theory and efficient solvers like Matlab and Mathematica.
منابع مشابه
A Linear Algebra Formulation for Boolean Satisfiability Testing
Boolean satisfiability (SAT) is a fundamental problem in computer science, which is one of the first proven NP-complete problems. Although there is no known theoretically polynomial time algorithm for SAT, many heuristic SAT methods have been developed for practical problems. For the sake of efficiency, various techniques were explored, from discrete to continuous methods, from sequential to pa...
متن کاملLinear Algebra with Sub-linear Zero-Knowledge Arguments
We suggest practical sub-linear size zero-knowledge arguments for statements involving linear algebra. Given commitments to matrices over a finite field, we give a sub-linear size zero-knowledge argument that one committed matrix is the product of two other committed matrices. We also offer a sub-linear size zero-knowledge argument for a committed matrix being equal to the Hadamard product of t...
متن کاملTowards Efficient Satisfiability Checking for Boolean Algebra with Presburger Arithmetic
Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that combines 1) Boolean algebra of sets of uninterpreted elements (BA) and 2) Presburger arithmetic (PA). BAPA can express relationships between integer variables and cardinalities of unbounded sets. In combination with other decision procedures and theorem provers, BAPA is useful for automatically verifying quantitative pr...
متن کاملTwenty-One Large Tractable Subclasses of Allen's Algebra
This paper continues Nebel and Burckert’s investigation of Allen’s interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P # NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is not decided. Four of them can express the notion of sequentiulity between intervals,...
متن کاملAllen Linear (Interval) Temporal Logic - Translation to LTL and Monitor Synthesis
The relationship between two well established formalisms for temporal reasoning is first investigated, namely between Allen’s interval algebra (or Allen’s temporal logic, abbreviated ATL) and linear temporal logic (LTL). A discrete variant of ATL is defined, called Allen linear temporal logic (ALTL), whose models are ω-sequences of timepoints. It is shown that any ALTL formula can be linearly t...
متن کامل