1,494 research outputs found
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
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