SEKE 2012 Proceedings - Knowledge Systems Institute

Modal ZIA, Modal Refinement Relation and
Logical Characterization
Zining Cao 1,2,3
1 College of Computer Science and Technology
Nanjing University of Aero. & Astro., Nanjing 210016, P. R. China
2 Provincial Key Laboratory for Computer Information Processing Technology
Soochow University, Suzhou 215006, P. R. China
3 National Key Laboratory of Science and Technology on Avionics System Integration
Shanghai 200233, P. R. China
Email: caozn@nuaa.edu.cn
Abstract—In this paper, we propose a specification approach
combining modal transition systems, interface automata and Z
language, named modal ZIA. This approach can be used to
describe temporal properties and data properties of software
components. We also study the modal refinement relation on
modal ZIAs. Then we propose a logic MZIAL for modal ZIAs
and give a logical characterization of modal refinement relation.
Finally, we present a sublogic of MZIAL, named muZIAL, and
give a model checking algorithm for finite modal ZIA.
Index Terms—interface automata; Z notation; modal transition
systems; refinement relation; modal logic; model checking
I. INTRODUCTION
Modern software systems are comprised of numerous components,
and are made larger through the use of software
frameworks. Such software systems exhibit various behavioral
aspects such as communication between components, and
state transformation inside components. Formal specification
techniques for such systems have to be able to describe all
these aspects. Unfortunately, a single specification technique
that is well suited for all these aspects is yet not available.
Instead one needs various specialized techniques that are very
good at describing individual aspects of system behavior. This
observation has led to research into the combination and
semantic integration of specification techniques.
Interface automata is a light-weight automata-based languages
for component specification, which was proposed in
[1]. An interface automaton (IA), introduced by de Alfaro and
Henzinger, is an automata-based model suitable for specifying
component-based systems. IA is part of a class of models
called interface models, which are intended to specify concisely
how systems can be used and to adhere to certain wellformedness
criteria that make them appropriate for modelling
component-based systems.
Z [15] is a typed formal specification notation based on
first order predicate logic and set theory. The formal basis
for Z is first order predicate logic extended with type set
theory. Using mathematics for specification is all very well
for small examples, but for more realistically sized problems,
things start to get out of hand. To deal with this, Z includes
the schema notation to aid the structuring and modularization
of specifications. A boxed notation called schemas is used
for structuring Z specifications. This has been found to be
necessary to handle the information in a specification of any
size. In particular, Z schemas and the schema calculus enable
a structured way of presenting large state spaces and their
transformation.
Modal transition systems [11], i.e., can be modelled as
automata whose transitions are typed with may and must
modalities. A modal transition system represents a set of
models; informally, a must transition is available in every
component that implements the modal transition system, while
a may transition needs not be. In [14], a unification of interface
automata and modal transition systems was presented.
In this paper, we present a new specification language which
combines modal transition systems, interface automata and Z
language. Interface automata are a kind of intuitive models for
interface property of software components. We combine modal
transition systems, interface and Z to describe modal property,
temporal property and data property in a unifying model. We
give the definition of modal ZIA. Roughly speaking, a modal
ZIA is in a style of modal interface automata but its states
and transitions are described by Z language. Furthermore, we
define the modal refinement relation between modal ZIAs and
give some propositions of such modal refinement relation.
Then we present a logic for modal ZIA and give a logical
characterization of modal refinement relation. Finally, we give
a model checking algorithm for finite modal ZIA.
This paper is organized as follows: Section 2 gives a brief
review of modal transition systems, interface automata and Z
language. In Section 3, we propose a specification languagemodal
ZIA. Furthermore, the modal refinement relation for
modal ZIA is presented and studied. In Section 4, we present a
logic MZIAL for modal ZIA and give a logical characterization
of modal refinement relation. In Section 5, we present a
sublogic of MZIAL, named muZIAL. Then we give a model
checking algorithm for finite modal ZIA. The paper is concluded
in Section 6.
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