Oded Goldreich’s 2000 paper “Candidate One-Way Functions Based on Expander Graphs” [4] describes a function that employs a fixed random predicate and an expander graph. Goldreich conjectures that this function is difficult to invert, but this difficulty does not seem to stem from any standard assumption in Complexity Theory. The task of inverting Goldreich’s function reduces naturally to a SAT ...

The Model Evolution (ME) Calculus is a proper lifting to first-order logic of the DPLL procedure, a backtracking search procedure for propositional satisfiability. Like DPLL, the ME calculus is based on the idea of incrementally building a model of the input formula by alternating constraint propagation steps with nondeterministic decision steps. One of the major conceptual improvements over ba...

The paper presents logical derivation algorithms that can be applied to inversion of polynomially computable discrete functions. The proposed approach is based on the fact that it is possible to organize DPLL derivation on a small subset of variables appeared in a CNF which encodes the algorithm computing the function. The experimental results showed that arrays of conflict clauses generated by...

We present a new string SMT solver, Z3str3, that is faster than its competitors Z3str2, Norn, CVC4, S3, and S3P over majority of three industrial-strength benchmarks, namely, Kaluza, PISA, and IBM AppScan. Z3str3 supports string equations, linear arithmetic over length function, and regular language membership predicate. The key algorithmic innovation behind the efficiency of Z3str3 is a techni...

Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause length k (k-SAT) can be classified into three styles: DPLL-like, PPSZ-like and Local Search, with local search algorithms having already been generalized to C...

FDPLL is a directly lifted version of the well-known DavisPutnam-Logeman-Loveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. non-ground and complementary literals now. The motivation for this lifting is to bring together successful first-order techniqu...

The paper is concerned with the computational evaluation and comparison of a new family of conflict-based branching heuristics for evolved DPLL Satisfiability solvers. Such a family of heuristics is based on the use of new scores updating criteria developed in order to overcome some of the typical unpleasant behaviors of DPLL search techniques. In particular, a score is associated with each lit...

dpll(t) is a central algorithm for Satisfiability Modulo Theories (smt) solvers. The algorithm combines results of reasoning about the Boolean structure of a formula with reasoning about conjunctions of theory facts to decide satisfiability. This architecture enables modern solvers to combine the performance benefits of propositional satisfiability solvers and conjunctive theory solvers. We cha...