10,269 research outputs found
Splitting Proofs for Interpolation
We study interpolant extraction from local first-order refutations. We
present a new theoretical perspective on interpolation based on clearly
separating the condition on logical strength of the formula from the
requirement on the com- mon signature. This allows us to highlight the space of
all interpolants that can be extracted from a refutation as a space of simple
choices on how to split the refuta- tion into two parts. We use this new
insight to develop an algorithm for extracting interpolants which are linear in
the size of the input refutation and can be further optimized using metrics
such as number of non-logical symbols or quantifiers. We implemented the new
algorithm in first-order theorem prover VAMPIRE and evaluated it on a large
number of examples coming from the first-order proving community. Our
experiments give practical evidence that our work improves the state-of-the-art
in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201
Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories
The problem of computing Craig Interpolants has recently received a lot of
interest. In this paper, we address the problem of efficient generation of
interpolants for some important fragments of first order logic, which are
amenable for effective decision procedures, called Satisfiability Modulo Theory
solvers.
We make the following contributions.
First, we provide interpolation procedures for several basic theories of
interest: the theories of linear arithmetic over the rationals, difference
logic over rationals and integers, and UTVPI over rationals and integers.
Second, we define a novel approach to interpolate combinations of theories,
that applies to the Delayed Theory Combination approach.
Efficiency is ensured by the fact that the proposed interpolation algorithms
extend state of the art algorithms for Satisfiability Modulo Theories. Our
experimental evaluation shows that the MathSAT SMT solver can produce
interpolants with minor overhead in search, and much more efficiently than
other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL
Efficient Interpolant Generation in Satisfiability Modulo Theories
The problem of computing Craig Interpolants for propositional (SAT) formulas has recently received a lot of interest, mainly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Although {some} works have addressed the topic of generating interpolants in SMT, the techniques and tools that are currently available have some limitations, and their performance still does not exploit the full power of current state-of-the-art SMT solvers. In this paper we try to close this gap. We present several techniques for interpolant generation in SMT which overcome the limitations of the current generators mentioned above, and which take full advantage of state-of-the-art SMT technology. These novel techniques can lead to substantial performance improvements wrt. the currently available tools. We support our claims with an extensive experimental evaluation of our implementation of the proposed techniques in the MathSAT SMT solver
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
Interpolation Properties and SAT-based Model Checking
Craig interpolation is a widespread method in verification, with important
applications such as Predicate Abstraction, CounterExample Guided Abstraction
Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model
checking techniques based on interpolation require collections of interpolants
to satisfy particular properties, to which we refer as "collectives"; they do
not hold in general for all interpolation systems and have to be established
for each particular system and verification environment. Nevertheless, no
systematic approach exists that correlates the individual interpolation systems
and compares the necessary collectives. This paper proposes a uniform
framework, which encompasses (and generalizes) the most common collectives
exploited in verification. We use it for a systematic study of the collectives
and of the constraints they pose on propositional interpolation systems used in
SAT-based model checking
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