arXiv subjects

Eugene Goldberg

Publications and source records attributed to Eugene Goldberg.

24 records · Page 2Linked to original sources

arXiv2015

Equivalence Checking and Simulation By Computing Range Reduction

We introduce new methods of equivalence checking and simulation based on Computing Range Reduction (CRR). Given a combinational circuit $N$, the CRR problem is to compute the set of outputs that disappear from the range of $N$ if a set of inputs of $N$ is excluded from consideration. Importantly, in many cases, range reduction can be efficiently found even if computing the entire range of $N$ is infeasible. Solving equivalence checking by CRR facilitates generation of proofs of equivalence that mimic a "cut propagation" approach. A limited version of such an approach has been successfully used by commercial tools. Functional verification of a circuit $N$ by simulation can be viewed as a way to reduce the complexity of computing the range of $N$. Instead of finding the entire range of $N$ and checking if it contains a bad output, such a range is computed only for one input. Simulation by CRR offers an alternative way of coping with the complexity of range computation. The idea is to exclude a subset of inputs of $N$ and compute the range reduction caused by such an exclusion. If the set of disappeared outputs contains a bad one, then $N$ is buggy.

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arXiv2014

Bug Hunting By Computing Range Reduction

We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if any). These clauses are derived by a technique called Partial Quantifier Elimination (PQE). Given a number n, the CRR method finds a counterexample of length less or equal to n or proves that such a counterexample does not exist. We show experimentally that a PQE-solver we developed earlier can be efficiently applied to derivation of constraining clauses for transition relations of realistic benchmarks. One of the most appealing features of the CRR method is that it can potentially find long counterexamples. This is the area where it can beat model checkers computing reachable states (or their approximations as in IC3) or SAT-based methods of bounded model checking. PQE cannot be efficiently simulated by a SAT-solver. This is important because the current research in model checking is dominated by SAT-based algorithms. The CRR method is a reminder that one should not put all eggs in one basket.

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arXiv2013

Verification of Sequential Circuits by Tests-As-Proofs Paradigm

We introduce an algorithm for detection of bugs in sequential circuits. This algorithm is incomplete i.e. its failure to find a bug breaking a property P does not imply that P holds. The appeal of incomplete algorithms is that they scale better than their complete counterparts. However, to make an incomplete algorithm effective one needs to guarantee that the probability of finding a bug is reasonably high. We try to achieve such effectiveness by employing the Test-As-Proofs (TAP) paradigm. In our TAP based approach, a counterexample is built as a sequence of states extracted from proofs that some local variations of property P hold. This increases the probability that a) a representative set of states is examined and that b) the considered states are relevant to property P. We describe an algorithm of test generation based on the TAP paradigm and give preliminary experimental results.

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arXiv2013

Quantifier Elimination by Dependency Sequents

We consider the problem of existential quantifier elimination for Boolean formulas in Conjunctive Normal Form (CNF). We present a new method for solving this problem called Derivation of Dependency-Sequents (DDS). A Dependency-sequent (D-sequent) is used to record that a set of quantified variables is redundant under a partial assignment. We introduce a resolution-like operation called join that produces a new D-sequent from two existing D-sequents. We also show that DDS is compositional, i.e. if our input formula is a conjunction of independent formulas, DDS automatically recognizes and exploits this information. We introduce an algorithm based on DDS and present experimental results demonstrating its potential.

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arXiv2012

Checking Satisfiability by Dependency Sequents

We introduce a new algorithm for checking satisfiability based on a calculus of Dependency sequents (D-sequents). Given a CNF formula F(X), a D-sequent is a record stating that under a partial assignment a set of variables of X is redundant in formula \exists{X}[F]. The D-sequent calculus is based on operation join that forms a new D-sequent from two existing D-sequents. The new algorithm solves the quantified version of SAT. That is, given a satisfiable formula F, it, in general, does not produce an assignment satisfying F. The new algorithm is called DS-QSAT where DS stands for Dependency Sequent and Q for Quantified. Importantly, a DPLL-like procedure is only a special case of DS-QSAT where a very restricted kind of D-sequents is used. We argue that this restriction a) adversely affects scalability of SAT-solvers and b) is caused by looking for an explicit satisfying assignment rather than just proving satisfiability. We give experimental results substantiating these claims.

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arXiv2012

Removal of Quantifiers by Elimination of Boundary Points

We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding resolvent clauses of F eliminating boundary points. This approach is similar to the method of quantifier elimination described in [9]. The difference of the method described in the present paper is twofold: {\bullet} branching is performed only on quantified variables, {\bullet} an explicit search for boundary points is performed by calls to a SAT-solver Although we published the paper [9] before this one, chrono- logically the method of the present report was developed first. Preliminary presentations of this method were made in [10], [11]. We postponed a publication of this method due to preparation of a patent application [8].

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