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Review of Computer Engineering Research

June 2020, Volume 7, 1, pp 27-37

Interactive Algorithms for the Verification of the Equality between Complex and Simplified Boolean-Algebra Expressions in Digital Decoders

Tochukwu Arinze Ikwunne

,

Samuel Obiora Okide

Tochukwu Arinze Ikwunne 1

Samuel Obiora Okide 2

  1. Alex Ekweme Federal University Ndufu-Aliike Ikwo, Nigeria 1

  2. Nnamdi Azikiwe University Awka, Nigeria 2

Pages: 27-37

DOI: 10.18488/journal.76.2020.71.27.37

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Article History:

Received: 14 January, 2020
Revised: 18 February, 2020
Accepted: 20 March, 2020
Published: 13 April, 2020


Abstract:

This work highlights the use of an algorithm in evaluating and verifying a complex Boolean expression that are used in fabricating digital decoder systems. Digital decoders are built by human beings and, unfortunately, humans make mistakes. Both design errors and faulty implementation may lead both the hardware and software components of systems to behave in unexpected ways, which in turn may lead to business losses and even risky situations. Karnough maps, Boolean algebra theorems and laws are some of the techniques that can be used to simplify and reduce complex Boolean algebra expressions and truth table can be used to confirm that the reduced Boolean algebra expression is the same as the original, complex Boolean algebra expression. However, generating the truth table manually is tedious, especially when the Boolean algebra equation or expression has many Boolean variables. Therefore, this work presents novel algorithms to verify and evaluate complex Boolean expression from the fabricated decoder circuit.
Contribution/ Originality
This study documents the importance of using an algorithmic approach in checking and evaluating the equality of a complex Boolean expression and its simplified form from the fabricated decoder circuit. This is to ensure that the hardware and software systems are designed with reduced or no errors.

Keywords:

Digital decoder, Boolean algebra expression, Seven-segmented display, Combinational logic gate, Verification, Algorithms, Applications.

Reference:

[1]          D. Tan, "On the structure of finite Boolean algebra," Journal of Mathematical Sciences & Mathematics Education, vol. 5, pp. 20-24, 2011.

[2]          O. E. Oguike, "Algorithms for verifying variants of boolean algebra equations and expressions," African Journal of Computing & ICT, vol. 6, pp. 1-8, 2013.

[3]          M. Dhar, "Fuzzy sets towards forming boolean algebra," International Journal of Energy, Information and Communications, vol. 2, pp. 1-22, 2011.

[4]          L. Rompis, "Boolean agebra for xor gates," Journal of Computer Science and Applications, vol. 1, pp. 14 - 16, 2013.

[5]          E. Clarke and E. Emerson, "Design and synthesis of synchronization skeletons using branching time temporal logic," in Proceedings of Workshop on Logics of Programs, Lecture Notes in Computer Science, Springer-Verlag, 1981, pp. 52–71.

[6]          J. Burch, E. M. Clarke, K. McMillan, D. Dill, and L. Hwang, "Symbolic model checking: 1020 states and beyond," in Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science, 1990, pp. 428–39.

[7]          G. Holzmann, Design and validation of computer protocols. Englewood Cliffs: Prentice Hall, Pearson Technology Group USA, 1990.

[8]          E. E. A. and C. Lei, "Efficient model checking in the fragments of the propositional μ-calculus," presented at the Symposion on Logic in Computer Science, IEEE Computer Society Press, 1986.

[9]          D. Long, A. Browne, E. Clarke, S. Jha, and W. Marrero, "An improved algorithm for the evaluation of fixpoint expressions," in Proceedings of International Conference on Computer Aided Verification (CAV’1994), Lecture Notes in Computer Science, Springer-Verlag, 1994, pp. 338–350.

[10]        H. Seidl, "Fast and simple nested fixpoints " Information Processing Letters, vol. 59, pp. 303–308, 1996. Available at: https://doi.org/10.1016/0020-0190(96)00130-5.

[11]        X. Liu, C. R. Ramakrishnan, and S. A. Smolka, "Fully local and efficient evaluation of alternating fixed points," in Proceedings of the 4th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Lecture Notes in Computer Science, Springer Verlag, 1998, pp. 5–19.

[12]        H. R. Andersen and B. Vergauwen, "Efficient checking of behavioural relations and modal assertions using fixed-point inversion," in Proceedings of Conference on Computer Aided Verification, Lecture Notes on Computer Science, Springer-Verlag, , 1995, pp. 142–154.

[13]        R. Cleaveland and B. Steffen, "Computing behavioural relations logically," in Proceedings of the 18th International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, Springer-Verlag, 1991, pp. 127–138.

[14]        K. Larsen, "Efficient local correctness checking," in Proceedings of Conference on Computer Aided Verification, Lecture Notes on Computer Science, Springer-Verlag, , 1992, pp. 30–43.

[15]        M. R. . "A generic on-the-fly solver for alternation-free boolean equation systems," in Proceedings of the 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’2003), Lecture Notes in Computer Science, Springer Verlag, 2003, pp. 81–96.

[16]        A. Mader, "Verification of modal properties using boolean equation systems," PhD Thesis, Technical University of Munich, 1997.

[17]        J. F. Groote and T. Willemse, "A checker for modal formulas for processes with data," in Proceedings of Formal Methods for Components and Objects, Second International Symposium (FMCO’2003), Lecture Notes in Computer Science, Springer-Verlag, 2004, pp. 223–239.

[18]        J. F. Groote and T. Willemse, "Parameterised boolean equation systems," in Proceedings of the 15th International Conference on Concurrency Theory (CONCUR’2004), Lecture Notes in Computer Science, Springer-Verlag, 2004, pp. 308–324.

[19]        J. F. Groote and T. Willemse, "Parameterised boolean equation systems," Theoretical Computer Science, vol. 343, pp. 332–369, 2005.

[20]        M. Azram, "Arithmetic version of boolean algebra," in Proceeding of 2nd IEEE Internation Conference on Computer Science and Information Technology, 2009, pp. 79 – 80.

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Funding:

This study received no specific financial support.

Competing Interests:

The authors declare that they have no competing interests.

Acknowledgement:

Both authors contributed equally to the conception and design of the study.

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