Microsoft Technology Licensing, LLC

Leonardo Mendonca De Moura

Nikolaj Skallerud Bjorner

Thomas J Ball

Vladimir A Levin

Eleonora O Bounimova

A method for automatically analyzing formulas and adding pattern annotations to quantifiers based on a database of common pattern idioms. The method involves matching base pattern inference for Satisfiability Modulo Theories (SMT) solvers. The method uses a database for fault detection in externally supplied pattern annotated formulas. The method also uses matching code trees to mixed second-order pattern matching.

Matching based pattern inference for SMT solvers

A system is described for processing predicates in the course of analyzing a program, based on a general-purpose theory of pointers. The system converts location expressions in the predicates into logical formulae that are interpretable by a theorem prover module, producing converted predicates. This conversion associates the location expressions with location objects. More specifically, the conversion represents variables as explicitly-specified location objects, and location terms (such as a field-type access terms and dereference-type terms) as constructor-specified location objects. The theory of pointers is also expressed by a set of axioms which constrain the operation of the theorem prover module.

Processing predicates including pointer information

Relevancy propagation for efficient theory combination is described. In one implementation, an efficient SMT solver dynamically applies relevancy propagation to limit propagation of unnecessary constraints in a DPLL-based solver. This provides a drastic increase in speed and performance over conventional DPLL-based solvers. The relevancy propagation is guided by relevancy rules, which in one implementation emulate Tableau rules for limiting constraint propagation, while maintaining the performance of efficient DPLL-based solvers. An exemplary solver propagates truth assignments to constraints of a formula, and tracks which truth assignments are relevant for determining satisfiability of the formula. The solver propagates truth assignments that were marked relevant to a theory solver, while avoiding propagation of irrelevant truth assignments. The efficient SMT solver provides a drastic reduction in search space covered during quantifier instantiation and offers profound acceleration during bit-vectors reasoning.

Relevancy propagation for efficient theory combination

Embodiments are introduced which provide for creation of an E-matching code tree index which works on E-graphs to make E-matching more efficient. Use of the E-matching code tree allows performing matching of several patterns simultaneously. Embodiments are also described which provide for the generation of inverted path indexes. An inverted path index may be used to filter an E-graph to determine terms which may potentially match patterns when an E-graph is updated.

E-matching for SMT solvers

A method is described for combining models of a plurality of theory solvers in order to produce a model which may be satisfiable by each of the plurality of theory solvers. A model is accessed for a first theory solver which is satisfiable in the first theory solver. It is determined that one or more equalities are implied by the model and it is determined if the equalities are compatible with a second solver. The model is updated in accordance any equalities determined not to be compatible with the second solver. A method is also described for mutation of models using freedom intervals. A freedom interval is determined for a variable within a model and the model is updates by choosing a value for the variable which lies within the freedom interval.

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Sammamish, WA, United States of America

Leonardo Mendonca De Moura