Download e-book for iPad: A Concise Introduction to Languages and Machines by Alan P. Parkes

Counting Numeration

By Alan P. Parkes

ISBN-10: 1848001207

ISBN-13: 9781848001206

This easy-to-follow textual content presents an obtainable creation to the most important subject matters of formal languages and summary machines inside of desktop technology. the writer follows the profitable formulation of his first e-book in this topic, this time making those center computing subject matters extra primary and offering a very good starting place for undergraduates.

The e-book is split into elements, Languages and Machines and Machines and Computation. the 1st half is worried with formal language idea, because it applies to machine technology, while half 2 considers the computational houses of the machines in additional aspect. this article is intentionally non-mathematical and, anywhere attainable, hyperlinks thought to sensible concerns, particularly the consequences for programming, computation and challenge fixing. Written in an off-the-cuff type, this textbook assumes just a uncomplicated wisdom of programming at the a part of the reader.

Features:

• transparent reasons of formal notation and jargon

• wide use of examples to demonstrate algorithms and proofs

• Pictorial representations of key concepts

• Chapter-opening overviews delivering an advent and advice to every topic

• An introductory bankruptcy offers the reader with a superior overview

• End-of-chapter workouts and solutions

This reader-friendly textbook has been written with undergraduates in brain and should be appropriate to be used on classes overlaying formal languages, computability, automata idea and computational linguistics. it's going to additionally make a good supplementary textual content for classes on set of rules complexity and compilers.

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Extra info for A Concise Introduction to Languages and Machines

Example text

AXb j ab Y ! bY c j bc A ! a j aA C ! c j cC: (a) Classify G according to the Chomsky hierarchy. (b) y Write a set definition of L(G). 54 3. Syntax, Semantics and Ambiguity (c)y Using the sentence a3b3c3 in L(G), show that G is an ambiguous grammar. You might like to justify this for yourself (hint: think about the derivation of sentences of the form aibici). 2. 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, and with particular reference to the example sentence, discuss the semantic implications of the ambiguity.

Are nonterminals, and that other items (if, then and else) are regarded as terminals. Now consider the following statement: if x > y then if y < z then x := x þ 1 else x := x { 1. Suppose that x > y and y < z are s, and that x := x þ 1 and x := x À 1 are s. Then two different parse trees can be constructed for our statement. 5 and is labelled ‘‘PARSE TREE 1’’. 6. We have two distinct structural accounts of a single sentence. This tells us that the grammar is ambiguous.

A grammar is fully defined when we know which symbols are terminals, which are non-terminals, and which of the non-terminals is the start symbol. In this book, we will usually see only the productions of a grammar, and we will assume the following: 30 2. Elements of Formal Languages l capitalised letters are non-terminal symbols l non-capitalised letters are terminal symbols l the capital letter S is the start symbol. The above will always be the case unless explicitly stated otherwise. 7 Phrase Structure Grammars and the Chomsky Hierarchy The production rules of the example grammar from the preceding section are simple in format.

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A Concise Introduction to Languages and Machines by Alan P. Parkes


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