### 15.11.15 - 20.11.15, Seminar 15471

# Symbolic Computation and Satisfiability Checking

### Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

## Motivation

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.