Synthesizing Multiple Boolean Functions using Interpolation on a Single Proof

It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to state that the visible behavior of the pipelined system should be identical to a non-pipelined reference system (Burch-Dill paradigm). We present a novel procedure to efficiently synthesize multiple Boolean control signals from a specification given as a quantified first-order formula (with a specific quantifier structure). Our approach uses uninterpreted functions to abstract details of the design. We construct an unsatisfiable SMT formula from the given specification. Then, from just one proof of unsatisfiability, we use a variant of Craig interpolation to compute multiple coordinated interpolants that implement the Boolean control signals. Our method avoids iterative learning and back-substitution of the control functions. We applied our approach to synthesize a controller for a simple two-stage pipelined processor, and present first experimental results.Comment: This paper originally appeared in FMCAD 2013, http://www.cs.utexas.edu/users/hunt/FMCAD/FMCAD13/index.shtml. This version includes an appendix that is missing in the conference versio

Invariant Synthesis for Incomplete Verification Engines

We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided inductive synthesis principle (CEGIS) and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates. Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties expressed in an expressive but undecidable separation logic. Our experiments show that our invariant synthesis framework based on non-provability information can both effectively synthesize inductive invariants and adequately strengthen contracts across a large suite of programs

Reduction of Interpolants for Logic Synthesis

Abstract—Craig Interpolation is a state-of-the-art technique for logic synthesis and verification, based on Boolean Satisfiability (SAT). Leveraging the efficacy of SAT algorithms, Craig Interpolation produces solutions quickly to challenging problems such as synthesizing functional dependencies and performing bounded model-checking. Unfortunately, the quality of the solutions is often poor. When interpolants are used to synthesize functional dependencies, the resulting structure of the functions may be unnecessarily complex. In most applications to date, interpolants have been generated directly from the proofs of unsatisfiability that are provided by SAT solvers. In this work, we propose efficient methods based on incremental SAT solving for modifying resolution proofs in order to obtain more compact interpolants. This, in turn, reduces the cost of the logic that is generated for functional dependencies. I