Our original aim for developing it was the need of a DPLL-based engine for our DPLL(T ) approach to Satisfiability Modulo Theories (SMT): deciding the satisfiability of ground first-order formulas with respect to background theories such as equality, linear integer or real arithmetic, arrays, etc. A DPLL(T ) system consists of a general DPLL(X) engine, very similar in nature to a SAT solver, wh...

SMT solvers have traditionally been based on the DPLL(T) algorithm, where the driving force behind the procedure is a DPLL search over truth valuations. This traditional framework allows for a degree of modularity in the treatment of theory solvers. Over time, theory solvers have become more and more closely integrated into the DPLL process, and consequently less and less modular. In this paper...

In the last two decades we have witnessed an impressive advance in the efficiency of propositional satisfiability techniques (SAT), which has brought large and previously-intractable problems at the reach of state-of-the-art SAT solvers. Most of this success is motivated by the impressive level of efficiency reached by current implementations of the DPLL procedure. Plain propositional logic, ho...

We propose two novel approaches for using CounterexampleGuided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented pr...

An overview is given of a number of recent developments in SAT and SAT Modulo Theories (SMT). In particular, based on our framework of Abstract DPLL and Abstract DPLL modulo Theories, we explain our DPLL(T) approach to SMT. Experimental results and future projects are discussed within BarcelogicTools, a set of logic-based tools developed by our research group in Barcelona. At the 2005 SMT compe...

Abstrract:For many application domains the best way to produce intelligent behavior is to encode knowledge about this domain to knowledge base. Verification of KB is one of the crucial issues in developing reliable knowledgebased systems. SAT techniques as resolution and DPLL can be used for verifying knowledge bases. We give a transformation of a DPLL refutation to a resolution refutation of a...

As the carrier frequency goes into terahertz band, phase noise of signal source has increasing impacts on performance communication system. Considering a 16QAM high-order digital modulation system (DMTCS), by comparing influence two kinds local oscillator sources with different characteristics bit error rate (BER) based theoretical analysis and experimental research, it is found that near-end g...

We present DPVIS, a Java tool to visualize the structure of SAT instances and runs of the DPLL (Davis-Putnam-Logemann-Loveland) procedure. DPVIS uses advanced graph layout algorithms to display the problem’s internal structure arising from its variable dependency (interaction) graph. DPVIS is also able to generate animations showing the dynamic change of a problem’s structure during a typical D...

The logic of equality with uninterpreted functions (EUF) and its extensions have been widely applied to processor verification, by means of a large variety of progressively more sophisticated (lazy or eager) translations into propositional SAT. Here we propose a new approach, namely a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given th...

Interpolation is a technique for extracting intermediate formulæ from a proof. It has applications in formal verification, where interpolation may enable a program analyser to discover information about intermediate program locations and states. We study interpolation in the theorem proving method DPLL(Γ+T ), which integrates tightly a superposition based prover Γ in a DPLL(T ) based SMT-solver...