2,097 research outputs found
FMplex: A Novel Method for Solving Linear Real Arithmetic Problems
In this paper we introduce a novel quantifier elimination method for
conjunctions of linear real arithmetic constraints. Our algorithm is based on
the Fourier-Motzkin variable elimination procedure, but by case splitting we
are able to reduce the worst-case complexity from doubly to singly exponential.
The adaption of the procedure for SMT solving has strong correspondence to the
simplex algorithm, therefore we name it FMplex. Besides the theoretical
foundations, we provide an experimental evaluation in the context of SMT
solving
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
An Instantiation-Based Approach for Solving Quantified Linear Arithmetic
This paper presents a framework to derive instantiation-based decision
procedures for satisfiability of quantified formulas in first-order theories,
including its correctness, implementation, and evaluation. Using this framework
we derive decision procedures for linear real arithmetic (LRA) and linear
integer arithmetic (LIA) formulas with one quantifier alternation. Our
procedure can be integrated into the solving architecture used by typical SMT
solvers. Experimental results on standardized benchmarks from model checking,
static analysis, and synthesis show that our implementation of the procedure in
the SMT solver CVC4 outperforms existing tools for quantified linear
arithmetic
Adapting Real Quantifier Elimination Methods for Conflict Set Computation
The satisfiability problem in real closed fields is decidable. In the context
of satisfiability modulo theories, the problem restricted to conjunctive sets
of literals, that is, sets of polynomial constraints, is of particular
importance. One of the central problems is the computation of good explanations
of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the
input constraints whose conjunction is already unsatisfiable. We adapt two
commonly used real quantifier elimination methods, cylindrical algebraic
decomposition and virtual substitution, to provide such conflict sets and
demonstrate the performance of our method in practice
The Potential and Challenges of CAD with Equational Constraints for SC-Square
Cylindrical algebraic decomposition (CAD) is a core algorithm within Symbolic
Computation, particularly for quantifier elimination over the reals and
polynomial systems solving more generally. It is now finding increased
application as a decision procedure for Satisfiability Modulo Theories (SMT)
solvers when working with non-linear real arithmetic. We discuss the potentials
from increased focus on the logical structure of the input brought by the SMT
applications and SC-Square project, particularly the presence of equational
constraints. We also highlight the challenges for exploiting these: primitivity
restrictions, well-orientedness questions, and the prospect of incrementality.Comment: Accepted into proceedings of MACIS 201
Generating Non-Linear Interpolants by Semidefinite Programming
Interpolation-based techniques have been widely and successfully applied in
the verification of hardware and software, e.g., in bounded-model check- ing,
CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various
work for discovering interpolants for propositional logic, quantifier-free
fragments of first-order theories and their combinations have been proposed.
However, little work focuses on discovering polynomial interpolants in the
literature. In this paper, we provide an approach for constructing non-linear
interpolants based on semidefinite programming, and show how to apply such
results to the verification of programs by examples.Comment: 22 pages, 4 figure
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