# Arjun Kapur

**Affiliations:** Graduate Student
Department of Computer Science
Stanford University

** Research Interests:** Formal Methods, Verification,
Hybrid Systems, Reliability, Software Engineering, Temporal Logics

## Abstracts

## Proving Safety Properties of Hybrid Systems

A. Kapur, T.A. Henzinger, Z. Manna, A. Pnueli
We propose a methodology for the specification, verification, and
design of hybrid systems. The methodology consists of the
computational model of *Concrete Phase Transition Systems*
(CPTSs), the specification language of * Hybrid Temporal
Logic* (HTL), the graphical system description language of *
Hybrid Automata*, and a proof system for verifying that hybrid
automata satisfy their HTL specifications.
The novelty of the approach lies in the continuous-time logic,
which allows specification of both point-based and interval-based
properties (ie. properties which describe changes over an interval)
and provides direct references to derivatives of variables,
and in the proof system that supports verification of point-based and
interval-based properties. The proof rules demonstrate that sound and
convenient induction rules can be established for continuous-time
logics. The proof rules are illustrated on several examples.

## Hybrid Diagrams: A Deductive-Algorithmic Approach to Hybrid
System Verification

L. de Alfaro, A. Kapur, Z. Manna
We present a methodology for the verification of temporal properties
of hybrid systems. The methodology is based on the deductive
transformation of *hybrid diagrams*, which represent the system
and its properties, and which can be algorithmically checked against
the specification. This check either gives a positive answer to the
verification problem, or provides guidance for the further
transformation of the diagrams. The resulting methodology is complete
for quantifier-free linear-time temporal logic.

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**Arjun Kapur's** home page.

Arjun Kapur
arjun@CS.Stanford.EDU