November 15 – 20 , 2015, Dagstuhl Seminar 15471

Symbolic Computation and Satisfiability Checking


Erika Abraham (RWTH Aachen, DE)
Pascal Fontaine (LORIA – Nancy, FR)
Thomas Sturm (MPI für Informatik – Saarbrücken, DE)
Dongming Wang (Beihang University – Beijing, CN)

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Dagstuhl Report, Volume 5, Issue 11 Dagstuhl Report
Aims & Scope
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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.

Summary text license
  Creative Commons BY 3.0 Unported license
  Erika Abraham, Pascal Fontaine, Thomas Sturm, and Dongming Wang

Related Dagstuhl Seminar


  • Data Structures / Algorithms / Complexity
  • Semantics / Formal Methods
  • Verification / Logic


  • Algorithmic algebra
  • Arithmetic
  • Automated reasoning
  • Decision procedures
  • Quantifier elimination
  • Satisfiability checking
  • SMT solving
  • Symbolic computation


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