## Section: New Software and Platforms

### The Redlog Computer Logic System

Participants : Thomas Sturm [contact] , Marek Košta.

Redlog is an integral part of the interactive computer algebra system Reduce. It supplements Reduce's comprehensive collection of powerful methods from symbolic computation by supplying more than 100 functions on first-order formulas. Redlog has been publicly available since 1995 and is constantly being improved. The name Redlog stands for Reduce Logic System. Andreas Dolzmann from Schloss Dagstuhl Leibniz-Zentrum is a co-developer of Redlog.

Reduce and Redlog are open-source and freely available under a modified BSD license at http://reduce-algebra.sourceforge.net/ . The Redlog homepage is located at http://www.redlog.eu/ . Redlog generally works with interpreted first-order logic in contrast to free first-order logic. Each first-order formula in Redlog must exclusively contain atoms from one particular Redlog-supported theory, which corresponds to a choice of admissible functions and relations with fixed semantics. Redlog-supported theories include Nonlinear Real Arithmetic (Real Closed Fields), Presburger Arithmetic, Parametric QSAT, and many more.

Effective quantifier elimination procedures for the various supported theories establish an important class of methods available in Redlog. For the theories supported by Redlog, quantifier elimination procedures immediately yield decision procedures. Besides these quantifier elimination-based decision methods there are specialized, and partly incomplete, decision methods, which are tailored to input from particular fields of application.

In 2014, Redlog made two important steps into distinct but equally important future directions. On the one hand, it integrated for the first time learning strategies, as they are known from CDCL-based SMT solving, into a classical real quantifier elimination procedure, viz. virtual substitution for linear formulas [28] . On the other hand, there was important progress concerning incomplete decision procedures for the reals. A journal submission currently under review describes identification of a Hopf bifurcation for the important MAPK model within less than a minute. The corresponding polynomial relevant for root-finding has dimension 10, total degree 100, and contains more than 850,000 monomials.

Redlog is a widely accepted tool and highly visible in mathematics, informatics, engineering and the sciences. The seminal article on Redlog [4] has received more than 300 citations in the scientific literature so far.