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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 607013, 12 pages
Research Article

A Deductive Approach towards Reasoning about Algebraic Transition Systems

1School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China
2Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China
3High Performance Network Lab, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Received 7 June 2015; Accepted 16 August 2015

Academic Editor: Krishnaiyan Thulasiraman

Copyright © 2015 Jun Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible.