By Krzysztof R. Apt

ISBN-10: 1475743769

ISBN-13: 9781475743760

ISBN-10: 1475743785

ISBN-13: 9781475743784

HIS e-book includes a such a lot accomplished textual content that provides syntax-directed and compositional tools for the formal veri?- T cation of courses. The method isn't really language-bounded within the feel that it covers a wide number of programming versions and contours that seem in most recent programming languages. It covers the sessions of - quential and parallel, deterministic and non-deterministic, disbursed and object-oriented courses. for every of the sessions it provides many of the c- teria of correctness which are appropriate for those sessions, resembling interference freedom, impasse freedom, and acceptable notions of liveness for parallel courses. additionally, targeted facts principles acceptable for every type of courses are provided. nonetheless range as a result of wealthy application sessions cons- ered, there exist a uniform underlying conception of veri?cation that's synt- orientated and promotes compositional techniques to veri?cation, resulting in scalability of the tools. The textual content moves the right kind stability among mathematical rigor and - dactic advent of more and more advanced principles in an incremental demeanour, accurately supported by means of state of the art examples. consequently it will possibly function a textbook for a number of classes on di?erent degrees and ranging periods. it will probably additionally function a reference publication for researchers within the concept of veri?- tion, particularly because it includes a lot fabric that by no means ahead of seemed in ebook shape. this is often in particular real for the remedy of object-oriented p- grams that is fullyyt novel and is strikingly stylish.

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**Additional info for Verification of Sequential and Concurrent Programs**

**Sample text**

Prove that P holds for n pothesis that P holds for n. + 1 from the induction hy- We can also use this induction principle to justify inductive definitions based on natural numbers. For example, consider once more the inductive definition of the n-fold relational composition Rn of a relation R on a set A. The implicit claim of this definition is: Rn is a well-defined relation on A for all n E No. The proof is by induction on n and is straightforward. A more interesting example is the following. 1 The inclusion R n ~ R* holds for all n E No.

Suzuki. The total correctness of parallel programs. SIAM Journal on Computing, pages 227-246, 1981. [Gri81] D. Gries. The Science of Programming. Springer-Verlag, New York,1981. R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12:576-580, 583, 1969. R. Hoare. Parallel programming: an axiomatic approach. Computer Languages, 1:151-160, 1975. R. Hoare. Communicating sequential processes. Communications of the ACM, 21:666-677, 1978. R. Hoare. Communicating Sequential Processes.

1. Mathematical Notation TUPLES In sets the repetition of elements and their order is irrelevant. If these things matter, we use another way of grouping elements: ordered pairs and tuples. For elements a and b, not necessarily distinct, (a, b) is an ordered pair or simply pair. Then a and b are called the components of (a, b). By definition, two pairs (a, b) and (c, d) are identical if and only if their first components and their second components agree. In symbols: (a, b) = (c, d) if and only if a = c and b = d.

### Verification of Sequential and Concurrent Programs by Krzysztof R. Apt

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