Campus Event Calendar

### A Quantifier- Elimination Heuristic for Octagonal Constraints

Deepak Kapur
University of New Mexico
SWS Colloquium

PhD (1980), Massachusetts Institute of Technology (MIT), Cambridge, MA;
M. Tech. (1973) and B. Tech. (1971), Indian Institute of Technology (IIT), Kanpur, India.

Chair, Department of Computer Science, University of New Mexico, Jan. 1999--June 2006.

School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India, 2003 onwards.

Professor, Department of Computer Science, Jan. 1988-- Dec. 1998, University at Albany.
Founder and former Director,
Institute for Programming and Logics, University at Albany.

Member, Research Staff, Computer Science Branch, General Electric Corporate Research and Development, Schenectady, NY, 1980-87.
AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI
Expert Audience
English

#### Date, Time and Location

Friday, 18 September 2015
14:00
-- Not specified --
G26
112
Kaiserslautern

#### Abstract

Octagonal constraints expressing weakly relational numerical
properties of the form ($l \le \pm x \pm y \leq h$) have been
found useful and effective in static analysis of numerical
programs. Their analysis serves as a key component of the tool
ASTREE based on abstract interpretation framework proposed by
Patrick Cousot and his group, which has been successfully used to
analyze commercial software consisting of hundreds of thousand of
lines of code. This talk will discuss a heuristic based on the
quantifier-elimination (QE) approach presented by Kapur (2005)
that can be used to automatically derive loop invariants
expressed as a conjunction of octagonal constraints in $O(n^2)$,
where $n$ is the number of program variables over which these
constraints are expressed. This is in contrast to the algorithms
developed in Mine's thesis which have the complexity at least
$O(n^3)$. The restricted QE heuristic usually generates
invariants stronger than those obtained by the freely available
Interproc tool. Extensions of the proposed approach to generating disjunctive
invariants will be presented.

Roslyn Stricker
0631 93039606
--email hidden