Virtual Substitution for SMT-Solving

Corzilius, Florian; Ábrahám, Erika

doi:10.1007/978-3-642-22953-4_31

Cited by 13 publications

(11 citation statements)

References 10 publications

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“…Secondly, our own SMT-solver based on our SMT-RAT (SMT Real-Arithmetic Toolbox) library [19], which we continuously improve and extend. The current release offers, besides some non-arithmetic components, the CArL [13] library for arithmetic datatypes and basic computations with them, and solver modules for simplex, the cylindrical algebraic decomposition [36], the virtual substitution method [18], Gröbner bases [33], interval constraint propagation, branch and bound, and their strategic combination [19].…”

Section: Arithmetic Theories In Smt Solversmentioning

confidence: 99%

Building Bridges between Symbolic Computation and Satisfiability Checking

Ábrahám

2015

Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

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The satisfiability problem is the problem of deciding whether a logical formula is satisfiable. For first-order arithmetic theories, in the early 20th century some novel solutions in form of decision procedures were developed in the area of mathematical logic. With the advent of powerful computer architectures, a new research line started to develop practically feasible implementations of such decision procedures. Since then, symbolic computation has grown to an extremely successful scientific area, supporting all kinds of scientific computing by efficient computer algebra systems.Independently, around 1960 a new technology called SAT solving started its career. Restricted to propositional logic, SAT solvers showed to be very efficient when employed by formal methods for verification. It did not take long till the power of SAT solving for Boolean problems had been extended to cover also different theories. Nowadays, fast SAT-modulo-theories (SMT) solvers are available also for arithmetic problems.Due to their different roots, symbolic computation and SMT solving tackle the satisfiability problem differently. We discuss differences and similarities in their approaches, highlight potentials of combining their strengths, and discuss the challenges that come with this task.

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Section: Arithmetic Theories In Smt Solversmentioning

confidence: 99%

Building Bridges between Symbolic Computation and Satisfiability Checking

Ábrahám

2015

Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

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“…Virtual substitution for the reals is well known in the satisfiability modulo theories (SMT) community. There it is typically employed in combination with DPLL(T) [46] as a component of theory solvers for linear and non-linear real arithmetic [1,2,13,14]. Independently, Redlog took part in the SMT-COMP 2017 competition and won the section for non-linear real arithmetic using plain virtual substitution with CAD as a fallback option when exceeding the degree bound.…”

Section: Impact Beyond Computer Algebramentioning

confidence: 99%

Thirty Years of Virtual Substitution

Sturm

2018

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation

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In 1988, Weispfenning published a seminal paper introducing a substitution technique for quantifier elimination in the linear theories of ordered and valued fields. The original focus was on complexity bounds including the important result that the decision problem for Tarski Algebra is bounded from below by a double exponential function. Soon after, Weispfenning's group began to implement substitution techniques in software in order to study their potential applicability to real world problems. Today virtual substitution has become an established computational tool, which greatly complements cylindrical algebraic decomposition. There are powerful implementations and applications with a current focus on satisfiability modulo theory solving and qualitative analysis of biological networks. CCS CONCEPTS • Computing methodologies → Equation and inequality solving algorithms; Algebraic algorithms;

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“…This allows for an easy extension of SMT-RAT by new solving techniques without knowledge about the overall architecture and other modules. Undergraduate students routinely implement new theory solver modules or extend existing ones for various logics in practical courses or as thesis projects [14,37,47,50,40,49,42,45,46,53,56,30,33,44,31].…”

Section: Smt-ratmentioning

confidence: 99%

“…The GBModule [38] uses a variant Gröbner bases to determine satisfiability over the reals. The virtual substitution method with various optimizations is implemented in the VSModule [15]. Another very popular method is interval constraint propagation that is available through the ICPModule [49].…”

Section: Previous Smt-rat Solver Modulesmentioning

confidence: 99%

Modular strategic SMT solving with SMT-RAT

Kremer

Ábrahám

2018

Acta Universitatis Sapientiae, Informatica

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In this paper we present the latest developments in SMT-RAT, a tool for the automated check of quantifier-free real and integer arithmetic formulas for satisfiability. As a distinguishing feature, SMT-RAT provides a set of solving modules and supports their strategic combination. We describe our CArL library for arithmetic computations, the available modules implemented on top of CArL, and how modules can be combined to satisfiability-modulo-theories (SMT) solvers. Besides the traditional SMT approach, some new modules support also the recently proposed and highly promising model-constructing satisfiability calculus approach.

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Virtual Substitution for SMT-Solving

Cited by 13 publications

References 10 publications

Building Bridges between Symbolic Computation and Satisfiability Checking

Building Bridges between Symbolic Computation and Satisfiability Checking

Thirty Years of Virtual Substitution

Modular strategic SMT solving with SMT-RAT

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