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Algorithmic Analysis of Array-Accessing Rajeev Alur, Pavol Cerny, and Scott Weinstein

Summary: Algorithmic Analysis of Array-Accessing
Rajeev Alur, Pavol Cern´y, and Scott Weinstein
University of Pennsylvania
Abstract. For programs whose data variables range over boolean or
finite domains, program verification is decidable, and this forms the ba-
sis of recent tools for software model checking. In this paper, we con-
sider algorithmic verification of programs that use boolean variables,
and in addition, access a single read-only array whose length is po-
tentially unbounded, and whose elements range over a potentially un-
bounded data domain. We show that the reachability problem, while un-
decidable in general, is (1) Pspace-complete for programs in which the
array-accessing for-loops are not nested, (2) decidable for a restricted
class of programs with doubly-nested loops. The second result establishes
connections to automata and logics defining languages over data words.
1 Introduction
Verification questions concerning programs are undecidable in general. However,
for finite-state programs -- programs whose data variables range over finite
types such as boolean, the number of bits needed to encode a program state is a


Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania


Collections: Computer Technologies and Information Sciences