Epilogue: Formal and informal correctness proofs

2020 ◽  
pp. 232-233
Author(s):  
Uri Abraham
Keyword(s):  
2021 ◽  
Vol 26 (6) ◽  
pp. 1-36
Author(s):  
Pushpita Roy ◽  
Ansuman Banerjee

Digital Microfluidics is an emerging technology for automating laboratory procedures in biochemistry. With more and more complex biochemical protocols getting mapped to biochip devices and microfluidics receiving a wide adoption, it is becoming indispensable to develop automated tools and synthesis platforms that can enable a smooth transformation from complex cumbersome benchtop laboratory procedures to biochip execution. Given an informal/semi-formal assay description and a target microfluidic grid architecture on which the assay has to be implemented, a synthesis tool typically translates the high-level assay operations to low-level actuation sequences that can drive the assay realization on the grid. With more and more complex biochemical assay protocols being taken up for synthesis and biochips supporting a wider variety of operations (e.g., MicroElectrode Dot Arrays (MEDAs)), the task of assay synthesis is getting intricately complex. Errors in the synthesized assay descriptions may have undesirable consequences in assay operations, leading to unacceptable outcomes after execution on the biochips. In this work, we focus on the challenge of examining the correctness of synthesized protocol descriptions, before they are taken up for realization on a microfluidic biochip. In particular, we take up a protocol description synthesized for a MEDA biochip and adopt a formal analysis method to derive correctness proofs or a violation thereof, pointing to the exact operation in the erroneous translation. We present experimental results on a few bioassay protocols and show the utility of our framework for verifiable protocol synthesis.


1981 ◽  
Vol 10 (137) ◽  
Author(s):  
Neil D. Jones ◽  
Henning Christiansen

<p>A simple algebra-based algorithm for compiler generation is described. Its input is a semantic definition of a programming language, and its output is a ''compiling semantics'' which maps each source program into a sequence of compile-time actions whose net effect on execution is the production of a semantically equivalent target program. The method does not require individual compiler correctness proofs or the construction of specialized target algebras.</p><p>Source program execution is assumed to proceed by performing a series of elementary actions on a runtime state. A semantic algebra is introduced to represent and manipulate possible execution sequences. A source semantic definition has two parts: A set of semantic equations mapping source programs into terms of the algebra, and an interpretation which gives concrete definitions of the state and the elementary actions on it.</p>


1983 ◽  
Vol 24 (2) ◽  
pp. 131-141 ◽  
Author(s):  
N. Soundararajan
Keyword(s):  

1986 ◽  
Vol 8 (2) ◽  
pp. 185-214 ◽  
Author(s):  
Laurian M. Chirica ◽  
David F. Martin
Keyword(s):  

A. Bertoni. Mathematical methods of the theory of stochastic automata. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 9–22. - R. V. Freivald. Functions computable in the limit by probabilistic machines. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 77–87. - B. Goetze and R. Klette. Some properties of limit recursive functions. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 88–90. - Ole-Johan Dahl. An approach to correctness proofs of semicoroutines. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 157–174. - G. Wechsung. The axiomatization problem of a theory of linear languages. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 298–302. - L. Banachowski. Modular approach to the logical theory of programs. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 327–332. - Pierangelo Miglioli. Mathematical foundations of motivation languages and synthesis maps. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 388–408. - H. Rasiowa. ω+-valued algorithmic logic as a tool to investigate procedures. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, pp. 423–450. - Andrzej Salwicki. Procedures, formal computations and models. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974 pp. 464–484.

1977 ◽  
Vol 42 (3) ◽  
pp. 422-423
Author(s):  
Steven S. Muchnick

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