Solution and Optimization of Systems of Pseudo-Boolean Constraints

Abstract

Abstract-Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, and so forth. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0-1 variables. Therefore, specialized 0-1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" (PB) constraints. This work provides an update on the on-going competition between generic ILP techniques and specialized 0-1 ILP techniques. To make a fair comparison, we generalize recent ideas for fast SAT-solving to more general 0-1 ILP problems that may include counting constraints and optimization. This generalization is embodied in our PB constraint solver and optimizer PBS, which is compared with state-of-the-art CNF and generic ILP solvers. Another aspect of our comparison is the evaluation on 0-1 ILP benchmarks that originate in Electronic Design Automation (EDA) but that cannot be directly solved by an SAT solver. Specifically, we solve instances of the Max-SAT and Max-ONEs optimization problems, which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively. Those problems have straightforward applications to SAT-based routing and are additionally important due to reductions from Max-Cut, Max-Clique, and Min Vertex Cover. Our experimental results show that specialized 0-1 techniques implemented in PBS tend to outperform generic ILP techniques on Boolean optimization problems, as well as on general EDA SAT problems.Index Terms-Boolean satisfiability (SAT), integer linear programming (ILP), backtrack search, conjunctive normal form (CNF), pseudo-Boolean (PB), Max-SAT, Max-ONE, global routing.

A SAT-based approach to solve the faculty course scheduling problem

“…The tool can handle an unlimited number of courses and faculty, allows the user to enter unique preferences for every course and is easily adaptable to any SAT solver. We used the SAT-based 0-1 ILP solver PBS [19]. It is an advanced SAT solver that employs the latest advances in the SAT technology and it can handle both CNF and PB constraints.…”

“…They have been found to be very efficient in expressing "counting constraints" [18]. Furthermore, PB extends SAT solvers, such as PBS [19], Bsolo [20], Pueblo [21] and MiniSAT+ [22], to handle optimization problems as opposed to only decision problems. This feature has introduced many new applications to the SAT domain.…”

Satisfiability Modulo the Theory of Costs: Foundations and Applications

“…Finally, we observe that also in this case binary search seems to be better than linear search. For PB problems it has been reported [5] that linear search is more effective than binary search. In our case, the opposite appears to be the case.…”

A Function Interaction Testing by Reusing Characterized Test Cases

“…2 Assume that each of test cases that verifies different execution paths of the function B is given as (1,2) and (3,7), where the first field of each tuple is an input and the second is an output. The behavior of the function B integrated with the function C is represented by the two test cases.…”

“…Unfortunately, the constraint solver depends on its symbolic reasoning capability and suffers from the path explosion problem in the case of analyzing plenty of the integrated source code with the deep call structure [3], [4]. The model checker similarly suffers from combinatorial blowup of the state space, commonly known as the state explosion problem [5].…”