Formal partitioning analysis and verification of extended algebraic automata

Algebraic automata is getting much importance in theoretical computer science because of its various applications, for example, in optimization of programs, verification of protocols, cryptography and modeling biological phenomena. Design of a complex system not only requires functionality but it also needs to capture its control behaviour. This paper is a part of our ongoing research on integration of algebraic automata and formal methods. Algebraic automaton is a powerful tool in modeling behaviour while Z is an ideal specification language used for describing statics of a system. Consequently, an integration of algebraic automata and Z will be a useful tool for modeling of complex systems. In this paper, we have described formal partitioning analysis of extended algebraic automata because of its use in components based modeling. At first, formal specification of constructing sub-automata for given automata is presented. Then equality of two given automata is verified. In next, cycles are identified and finally formal partitioning analysis of extended algebraic automata is provided. The formal specification is checked, analyzed and validated using Z/Eves tool. Key words: Algebraic automata, partitioning automata, component based modeling, Z notation, validation.

[1]  D. J. Creasey,et al.  The importance of formal specification in the design of hardware systems , 1994 .

[2]  Sofiène Tahar,et al.  Verification of Probabilistic Properties in HOL Using the Cumulative Distribution Function , 2007, IFM.

[3]  Nazir Ahmad Zafar,et al.  Construction of Intersection of Nondeterministic Finite Automata using Z Notation , 2008 .

[4]  Daniel I. A. Cohen,et al.  Introduction to computer theory , 1986 .

[5]  Hossam A. Gabbar.  Fundamentals of Formal Methods , 2006 .

[6]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[7]  Monika Heiner,et al.  Modeling Safety-Critical Systems with Z and Petri Nets , 1999, SAFECOMP.

[8]  Wang Yi,et al.  Timed Patterns: TCOZ to Timed Automata , 2004, ICFEM.

[9]  Nazir Ahmad Zafar,et al.  Formal Proof of Equivalence in Endomorphisms and Automorphisms over Strongly Connected Automata , 2008, 2008 International Conference on Computer Science and Software Engineering.

[10]  Robert L. Constable,et al.  Constructively formalizing automata theory , 2000, Proof, Language, and Interaction.

[11]  A. Isazadeh.  SOFTWARE ENGINEERING: INTEGRATION* , 2004 .

[12]  Byoungmoon Chin,et al.  Automated Test Generation from Specifications Based on Formal Description Techniques , 1997 .

[13]  Sofiène Tahar,et al.  Formalization of Cadence SPW Fixed-Point Arithmetic in HOL , 2002, IFM.

[14]  Nancy A. Lynch,et al.  The Theory of Timed I/o Automata , 2003 .

[15]  W. Wechler.  The concept of fuzziness in automata and language theory , 1978 .

[16]  John Derrick,et al.  Structural Refinement in Object-Z/CSP , 2000, IFM.

[17]  Jong-Hun Lee,et al.  A Bimodal Approach for Land Vehicle Localization , 2004 .

[18]  A. Ali,et al.  Linking Finite Automata and Formal Methods Enhancing Modeling Power for Complex Systems , 2008, 2008 International Conference on Computer Science and Information Technology.

[19]  Jin Song Dong,et al.  Integrating Object-Z with timed automata , 2005, 10th IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'05).

[20]  K. Peeva.  Fuzzy automata and languages: theory and applications , 2004 .

[21]  Nazir Ahmad Zafar,et al.  Formal Construction of Deterministic Finite Automata Recognizing Intersection of Regular Languages , 2008, Software Engineering Research and Practice.

[22]  Wolfgang Grieskamp,et al.  A Modular Framework for the Integration of Heterogeneous Notations and Tools , 1999, IFM.

[23]  Bill Stoddart,et al.  Integrated Formal Methods , 2001, Lecture Notes in Computer Science.

[24]  C. J. Burgess.  The Role of Formal Methods in Software Engineering Education and Industry , 1995 .

[25]  Joël Ouaknine,et al.  State/Event-Based Software Model Checking , 2004, IFM.

[26]  Xudong He,et al.  PZ nets a formal method integrating Petri nets with Z , 2001, Inf. Softw. Technol..

[27]  Anthony Hall.  Correctness by Construction: Integrating Formality into a Commercial Development Process , 2002, FME.

[28]  Jeanine Souquières,et al.  Integration of UML Views using B Notation , 2002 .

[29]  Claudio L. Lucchesi,et al.  Applications of finite automata representing large vocabularies , 1993, Softw. Pract. Exp..