Mechanizing Verification of Arithmetic Circuits: SRT Division

作者: Deepak Kapur , M. Subramaniam

DOI: 10.1007/BFB0058026

关键词: Division (mathematics)AdderPresburger arithmeticAutomated theorem provingNumber theoryRewritingCorrectnessComputer sciencePentiumProgramming language

摘要: The use of a rewrite-based theorem prover for verifying properties arithmetic circuits is discussed. A such as Rewrite Rule Laboratory (RRL) can be used effectively establishing numbertheoretic adders, multipliers and dividers. Since verification adders has been discussed elsewhere in earlier papers, the focus this paper on divider circuit. An SRT division circuit similar to one Intel Pentium processor mechanically verified using RRL. number-theoretic correctness established from its equational specification. proof generated automatically, follows easily inference procedures contextual rewriting decision procedure quantifier-free theory numbers (Presburger arithmetic) already implemented Additional enhancements provers RRL that would further facilitate with structure are

参考文章(20)
Stanford University. Computer Systems Laboratory, An Analysis of Division Algorithms and Implementations Stanford University. ,(1995)
Deepak Kapur, Rewriting, Decision Procedures and Lemma Speculation for Automated Hardware Verification theorem proving in higher order logics. pp. 171- 182 ,(1997) , 10.1007/BFB0028393
Amos R. Omondi, Computer arithmetic systems: algorithms, architecture and implementation Prentice Hall International (UK) Ltd.. ,(1994)
Harald Rueß, Natarajan Shankar, Mandayam K Srivas, Modular Verification of SRT Division computer aided verification. pp. 123- 134 ,(1996) , 10.1007/3-540-61474-5_63
Hantao Zhang, Implementing Contextual Rewriting CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems. pp. 363- 377 ,(1992) , 10.1007/3-540-56393-8_28
Hantao Zhang, Deepak Kapur, Mukkai S Krishnamoorthy, A Mechanizable Induction Principle for Equational Specifications conference on automated deduction. pp. 162- 181 ,(1988) , 10.1007/BFB0012831
Tomas Lang, MiloTs Dragutin Ercegovac, Division and Square Root: Digit-Recurrence Algorithms and Implementations Kluwer Academic Publishers. ,(1994)
Edmund M. Clarke, Steven M. German, Xudong Zhao, Verifying the SRT Division Algorithm Using Theorem Proving Techniques formal methods. ,vol. 14, pp. 7- 44 ,(1999) , 10.1023/A:1008665528003
Paul S. Miner, James F. Leathrum, Verification of IEEE Compliant Subtractive Division Algorithms formal methods in computer aided design. pp. 64- 78 ,(1996) , 10.1007/BFB0031800
K. D. TOCHER, TECHNIQUES OF MULTIPLICATION AND DIVISION FOR AUTOMATIC BINARY COMPUTERS Quarterly Journal of Mechanics and Applied Mathematics. ,vol. 11, pp. 364- 384 ,(1958) , 10.1093/QJMAM/11.3.364