Dagstuhl Seminar 15471
Symbolic Computation and Satisfiability Checking
( Nov 15 – Nov 20, 2015 )
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https://www.dagstuhl.de/15471
Organizers
- Erika Abraham (RWTH Aachen, DE)
- Pascal Fontaine (LORIA - Nancy, FR)
- Thomas Sturm (MPI für Informatik - Saarbrücken, DE)
- Dongming Wang (Beihang University - Beijing, CN)
Contact
- Andreas Dolzmann (for scientific matters)
- Dagmar Glaser (for administrative matters)
Impacts
- SC2 : Satisfiability Checking Meets Symbolic Computation : article in LNAI 9791 "Intelligent Computer Mathematics : CICM 2016" : pp. 28-43 - Abraham, Erika; Abbott, John; Bigatti, Anna M.; England, Matthew; Forrest, Stephen; Sturm, Thomas; Seiler, Werner M. ; Kroening, Daniel; Griggio, Alberto; Fontaine, Pascal; Davenport, James Harold; Cimatti, Alessandro; Buchberger, Bruno; Brain, Martin; Becker, Bernd - Berlin : Springer, 2016 - (Lecture notes in artificial intelligence ; 9791 : article).
- Solving Nonlinear Integer Arithmetic with MCSAT : article in LNCS 10145 "Model Checking, and Abstract Interpretation : VMCAI 2017" : pp. 330-346 - Jovanovic, Dejan - Berlin : Springer, 2014 - (Lecture notes in computer science ; 10145 : article).
The development of decision procedures for arithmetic theories started in the early 20th century in the area of mathematical logic. In the second half of the 20th century it played a prominent role within the development of algebraic model theory. Around 1970 one important research line shifted its focus from theoretical results towards practically feasible procedures. That research line was one of the origins of an area known today as symbolic computation or computer algebra.
More recently, the satisfiability checking community, which originated from propositional SAT solving and which is surprisingly disconnected from symbolic computation, began to develop highly interesting results with a particular focus on existential decision problems, following the track of SAT solving towards industrial applications. Powerful satisfiability modulo theories (SMT) solvers were developed, which enrich propositional SAT solving with components for different theories. We understand satisfiability checking in a broad sense, covering besides SMT solving also theorem proving with arithmetic.
The two communities of symbolic computation and satisfiability checking are quite disjoint, despite strong reasons for them to discuss together. The communities share interests (e.g. examining arithmetic expressions) that are central to both. The goal of this Dagstuhl Seminar is to foster cross-fertilization of both fields and bring improvements for both satisfiability checking and symbolic computation, and for their applications.
More specifically, some questions to address are:
- What is the state-of-the-art for solving arithmetic problems in the two communities? What are general analogies, what are the differences?
- What are relevant yet unsolved problems in the two communities?
- Which successful techniques are transferable between the communities to solve open challenges? What are the requirements for transferability?
- How can certain transferable techniques be adapted to be applicable in the new domain?
- Which benchmarks known in one of the communities could be used in the other community as well?
Special attention will be given to industrial applications of arithmetic reasoning.
The seminar focused on satisfiability checking for combinations of first-order logic and subclasses thereof with arithmetic theories in a very liberal sense, also covering quantifiers and parameters.
The development of decision procedures for corresponding theories started in the early 20th century in the area of mathematical logic. In the second half of the 20th century it played a prominent role within the development of algebraic model theory. Finally, around 1970, one important research line, viz. algebraic decision methods for real arithmetics, shifted its focus from theoretical results towards practically feasible procedures. That research line was one of the origins of an area known today as symbolic computation or computer algebra.
More recently, the satisfiability checking community, which originated from propositional SAT solving and which is surprisingly disconnected from symbolic computation, began to develop highly interesting results with a particular focus on existential decision problems, following the track of SAT solving towards industrial applications. Powerful satisfiability modulo theories (SMT) solvers were developed, which enrich propositional SAT solving with components for different theories. We understand satisfiability checking in a broad sense, covering besides SMT solving also theorem proving with arithmetic.
The two communities of symbolic computation and satisfiability checking have been quite disjoint, despite strong reasons for them to discuss together. The communities share interests, e.g., examining arithmetic expressions, that are central to both. As a matter of fact, the symbolic computation community has been mostly unaware of basic insights in the satisfiability checking community, such as the efficiency of conflict-driven search with learning, as well as of their fundamental requirements, e.g., incrementality or explanations in the unsatisfiable case. Vice versa, researchers in satisfiability checking have adopted decision procedures from symbolic computation, such as CAD for real closed field, only quite naively, so that they do not really benefit from the considerable experience gained by the original community during 45 years. It is our hope that our seminar contribute to bringing the two communities together, and that they will be much stronger at tackling problems that currently defeat them both, separately.
The seminar offered its participants an opportunity to exchange knowledge about existing methods and applications, to push forward the communication of needs and interests, and to draw attention to challenging open research questions. The participants included researchers from all relevant research areas and with affiliations in academia and as well as in industry. The program was a balanced combination of presentations and tutorials, but also offering time for small group discussions and exchange of ideas.
To the best of our knowledge, the seminar was the first global meeting of the two communities of symbolic computation and satisfiability checking. We are confident that it will initiate cross-fertilization of both fields and bring improvements for both satisfiability checking and symbolic computation, and for their applications.
Creative Commons BY 3.0 Unported license
Erika Abraham, Pascal Fontaine, Thomas Sturm, and Dongming Wang
- John Abbott (Universität Kassel, DE) [dblp]
- Erika Abraham (RWTH Aachen, DE) [dblp]
- Bernd Becker (Universität Freiburg, DE) [dblp]
- Martin Bromberger (MPI für Informatik - Saarbrücken, DE) [dblp]
- Christopher W. Brown (U.S. Naval Academy - Annapolis, US) [dblp]
- Shaowei Cai (Chinese Academy of Sciences - Beijing, CN) [dblp]
- Florian Corzilius (RWTH Aachen, DE) [dblp]
- James H. Davenport (University of Bath, GB) [dblp]
- Pascal Fontaine (LORIA - Nancy, FR) [dblp]
- Stephen Forrest (Maplesoft Europe GmbH, DE) [dblp]
- Jürgen Gerhard (Maplesoft - Waterloo, CA) [dblp]
- Maximilian Jaroschek (MPI für Informatik - Saarbrücken, DE) [dblp]
- Dejan Jovanovic (SRI - Menlo Park, US) [dblp]
- Tim King (Google Inc. - Mountain View, US) [dblp]
- Konstantin Korovin (University of Manchester, GB) [dblp]
- Marek Kosta (MPI für Informatik - Saarbrücken, DE) [dblp]
- Laura Kovács (Chalmers UT - Göteborg, SE) [dblp]
- Gereon Kremer (RWTH Aachen, DE) [dblp]
- Wolfgang Küchlin (Universität Tübingen, DE) [dblp]
- Viktor Levandovskyy (RWTH Aachen, DE) [dblp]
- Klaus Meer (BTU Cottbus, DE) [dblp]
- David Monniaux (VERIMAG - Grenoble, FR) [dblp]
- Chenqi Mou (Beihang University - Beijing, CN) [dblp]
- Mizuhito Ogawa (JAIST - Ishikawa, JP) [dblp]
- Andrew Reynolds (EPFL - Lausanne, CH) [dblp]
- Yosuke Sato (Tokyo University of Science, JP) [dblp]
- Karsten Scheibler (Universität Freiburg, DE) [dblp]
- Tobias Schubert (Universität Freiburg, DE) [dblp]
- Viorica Sofronie-Stokkermans (Universität Koblenz-Landau, DE) [dblp]
- Thomas Sturm (MPI für Informatik - Saarbrücken, DE) [dblp]
- Laurent Voisin (SYSTEREL Aix en Provence, FR) [dblp]
- Christoph M. Wintersteiger (Microsoft Research UK - Cambridge, GB) [dblp]
- Patrick Wischnewski (Logic4Business - Saarbrücken, DE) [dblp]
- Kazuhiro Yokoyama (Rikkyo University - Tokyo, JP) [dblp]
Related Seminars
- Dagstuhl Seminar 22072: New Perspectives in Symbolic Computation and Satisfiability Checking (2022-02-13 - 2022-02-18) (Details)
Classification
- data structures / algorithms / complexity
- semantics / formal methods
- verification / logic
Keywords
- algorithmic algebra
- arithmetic
- automated reasoning
- decision procedures
- quantifier elimination
- satisfiability checking
- SMT solving
- symbolic computation
