# A Concise Introduction to Languages and Machines (Undergraduate Topics in Computer Science)

Language: English

Pages: 346

ISBN: 1848001207

Format: PDF / Kindle (mobi) / ePub

A Concise Introduction to Languages, Machines and Logic provides an accessible introduction to three key topics within computer science: formal languages, abstract machines and formal logic. Written in an easy-to-read, informal style, this textbook assumes only a basic knowledge of programming on the part of the reader.

The approach is deliberately non-mathematical, and features: - Clear explanations of formal notation and jargon, - Extensive use of examples to illustrate algorithms and proofs, - Pictorial representations of key concepts, - Chapter opening overviews providing an introduction and guidance to each topic, - End-of-chapter exercises and solutions, - Offers an intuitive approach to the topics.

This reader-friendly textbook has been written with undergraduates in mind and will be suitable for use on course covering formal languages, formal logic, computability and automata theory. It will also make an excellent supplementary text for courses on algorithm complexity and compilers.

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T, z2N Informal description and examples The definition of PSGs we have already seen. Anything allowed on the left-hand side (except for e), anything allowed on the right. All of our example grammars considered so far conform to this. Example type 0 production: aXYpq ! aZpq (all productions of G1, G2 and G3 conform { but see below). As for type 0, but we are not allowed to have e on the left- or the right-hand sides. Note that the example production given for type 0 is not a context sensitive.

Implication of the ambiguity. Formally, ambiguity in a language is reflected in the existence of more than one parse tree for one or more sentences of that language. To illustrate this, let us consider an example that relates to a programming language called Algol60, a language that influenced the designers of Pascal. The example also applies to Pascal itself and is based on the following fragment of a programming language definition, for which we revert, for convenience, to the BNF notation.

Ambiguous if L(G) contains any sentence which has two or more distinct derivation trees. Correspondingly: A PSG, G, is unambiguous if L(G) contains no sentences which have two or more distinct derivation trees. If we find any sentence in L(G) which has two or more derivation trees, we have established that our grammar is ambiguous. Sometimes, an ambiguous grammar 3.5 Ambiguity 53 can be replaced by an unambiguous grammar which does the same job (i.e. generates exactly the same language). This.

Any context free grammar that generates it is necessarily ambiguous.You might like to justify this for yourself (hint: think about the derivation of sentences of the form aibici). 3.2. Given the following productions of a grammar, G: S!E E ! T jE þ T jT À E T ! 1j2j3 ðnote that 1; 2; 3; þand - are terminal symbolsÞ; and the following sentence in L(G): 3{2þ1 (a) use the sentence to show that G is an ambiguous grammar (b)y assuming the standard arithmetic interpretation of the terminal symbols,.

LLC j LL j KB j b J!a K!b L ! c: The new productions are again underlined. You can verify that what we have done has not changed the terminal strings that can be generated from Z. We are now ready for the final step. 102 5. Context Free Languages and Pushdown Recognisers Step 3: Productions with more than two non-terminals on the right-hand side. After steps 1 and 2, all our productions will be of the form: x ! y or x ! z where y consists of two or more non-terminals and z is a single.