Formal Specification and Implementation of Priority Queue using Stream Functions

Formal Specification and Implementation of Priority Queue using Stream Functions

Gongzhu Hu, Jin Zhang, Roger Lee
Copyright: © 2013 |Pages: 10
DOI: 10.4018/ijsi.2013070105
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Abstract

Formal specification of software components, as a core research area in software engineering, has been widely studied for decades. Although quite a few formal models have been proposed for this purpose, specification of concrete software components is still a challenging task due to the complexity of the functionalities of the components. In this paper, the authors use the stream function model to specify the behavior of priority queue, a commonly used software component. This specification formally defines the regular behavior and fault tolerance behavior of priority queue. In particular, a priority-concatenation operator is defined to handle the ordering of data items to ensure the highest-priority item is removed first. A finite state machine is built based on this specification as an implementation of priority queue. In addition, the authors also discuss a priority upgrading approach to handle possible starvation situation of low-priority data items in the priority queue.
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Stream Function

First, we briefly review the basic concept of stream function as formal model for component specification.

Given an alphabet A, the set A* comprises all streams A = (α1, α2, …, αk) of length

|A| = k with element αiijsi.2013070105.m01. Several operations can be applied to communication streams, one of the basic operator is concatenation defined as& . A* x A* → A*of two streams A = (α1, α2, …, αk) and B = (b1, b2, …, bk), that yields the stream

A & B = (α1, α2, …, αk, b1, b2, …, bk) (1)

A stream function f . A* → B* maps an input stream to an output stream (Stephens, 1997).

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