SC-square: when Satisfiability Checking and Symbolic Computation join forces

Ábrahám, Erika; Abbott, John; Becker, Bernd; Bigatti, Anna Maria; Brain, Martin; Cimatti, Alessandro; Davenport, James H.; England, Matthew; Fontaine, Pascal; Forrest, Stephen; Griggio, Alberto; Kroening, Daniel; Seiler, Werner M.

doi:10.29007/p319

Cited by 3 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…procedures do not comply with the incremental, backtracking and explanation of inconsistencies properties expected of SMT-compliant theory solvers. One interesting project to look at is SC 2 [2], whose goal is to create a new community aiming at bridging the gap between symbolic computation and satisfiability checking, combining the strengths of both worlds in order to pursue problems currently beyond their individual reach. Further opportunities to increase efficiency when tackling non-linear expressions might be found in the recent advances in symbolic-numeric computation [56].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A Survey of Symbolic Execution Techniques

et al. 2018

View full text Add to dashboard Cite

Many security and software testing applications require checking whether certain properties of a program hold for any possible usage scenario. For instance, a tool for identifying software vulnerabilities may need to rule out the existence of any backdoor to bypass a program's authentication. One approach would be to test the program using different, possibly random inputs. As the backdoor may only be hit for very specific program workloads, automated exploration of the space of possible inputs is of the essence. Symbolic execution provides an elegant solution to the problem, by systematically exploring many possible execution paths at the same time without necessarily requiring concrete inputs. Rather than taking on fully specified input values, the technique abstractly represents them as symbols, resorting to constraint solvers to construct actual instances that would cause property violations. Symbolic execution has been incubated in dozens of tools developed over the last four decades, leading to major practical breakthroughs in a number of prominent software reliability applications. The goal of this survey is to provide an overview of the main ideas, challenges, and solutions developed in the area, distilling them for a broad audience.If you are considering citing this survey, we would appreciate if you could use the following BibTeX entry: http://goo.gl/Hf5Fvc 0:2 R. Baldoni et al.

show abstract

Section: Discussionmentioning

confidence: 99%

“…We refer the interested reader to[13] for an exhaustive introduction to SMT solving, and to[2] for a discussion of its distinctive strengths. ACM Computing Surveys, Vol.…”

mentioning

confidence: 99%

A Survey of Symbolic Execution Techniques

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Let (A, B) be a complex Golay sequence pair. Then resum(A) 2 + imsum(A) 2 + resum(B) 2 + imsum(B) 2 = 2n.…”

Section: ( [19]mentioning

confidence: 99%

“…This method combines both computer algebra and SAT solving and is of interest in its own right because it links the two previously separated fields of symbolic computation and satisfiability checking. Recently there has been interest in combining methods from both fields to solve computational problems as demonstrated by the SC 2 project [1,2]. Our work fits into this paradigm and to our knowledge is the first application of a SAT solver to search for complex Golay pairs, though previous work exists which uses a SAT solver to search for other types of complementary sequences [3][4][5]31].…”

Section: Introductionmentioning

confidence: 99%

Enumeration of Complex Golay Pairs via Programmatic SAT

Bright

Kotsireas

Heinle

2018

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

Self Cite

View full text Add to dashboard Cite

We provide a complete enumeration of all complex Golay pairs of length up to 25, verifying that complex Golay pairs do not exist in lengths 23 and 25 but do exist in length 24. This independently verifies work done by F. Fiedler in 2013 [11] that confirms the 2002 conjecture of Craigen, Holzmann, and Kharaghani [8] that complex Golay pairs of length 23 don't exist. Our enumeration method relies on the recently proposed SAT+CAS paradigm of combining computer algebra systems with SAT solvers to take advantage of the advances made in the fields of symbolic computation and satisfiability checking. The enumeration proceeds in two stages: First, we use a fine-tuned computer program and functionality from computer algebra systems to construct a list containing all sequences which could appear as the first sequence in a complex Golay pair (up to equivalence). Second, we use a programmatic SAT solver to construct all sequences (if any) that pair off with the sequences constructed in the first stage to form a complex Golay pair.

show abstract

“…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

View full text Add to dashboard Cite

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;

show abstract

SC-square: when Satisfiability Checking and Symbolic Computation join forces

Cited by 3 publications

References 13 publications

A Survey of Symbolic Execution Techniques

A Survey of Symbolic Execution Techniques

Enumeration of Complex Golay Pairs via Programmatic SAT

Thirty Years of Virtual Substitution

Contact Info

Product

Resources

About