Mathematical Aspects of Computer ScienceJacob T. Schwartz, American Mathematical Society American Mathematical Soc., Dec 31, 1967 - 224 pages |
Contents
| 1 | |
ASSIGNING MEANINGS TO PROGRAMS | 19 |
CORRECTNESS OF A COMPILER FOR ARITHMETIC EXPRESSIONS₂ | 33 |
CONTEXTFREE LANGUAGES AND TURING MACHINE COMPUTATIONS | 42 |
COMPUTER ANALYSIS OF NATURAL LANGUAGES₁ | 52 |
THE USE OF COMPUTERS IN THE THEORY OF NUMBERS | 111 |
A MACHINE CALCULATION OF A SPECTRAL SEQUENCE | 117 |
NUMERICAL HYDRODYNAMICS OF THE ATMOSPHERE | 125 |
THE CALCULATION OF ZEROS OF POLYNOMIALS AND ANALYTIC FUNCTIONS | 138 |
MATHEMATICAL THEORY OF AUTOMATA | 153 |
LINEARLY UNRECOGNIZABLE PATTERNS₁ | 176 |
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Common terms and phrases
A₁ algebra algorithm analysis applied assigned atoms automata theory automaton axioms bachelor base component Briggs Stadium calculation clauses coefficients compiler complements complex symbol computation condition connected consider contains context-free grammar context-free languages corresponding cut-point decision problem defined denote derived phrase-marker elements equations equivalence example finite set flowchart G polynomials geometric given integers interpretation isolated cut-point iteration function L₁ latent clashes lexical linear linguistics masks Math mathematical natural languages node noun obtained operation P₁ perceptron phrase structure phrase-marker polynomials predicate probabilistic automata Proc procedure proof recursion regular expressions result rewriting satisfy semantic definition semantic markers sentence sequence statement structural index subcategorization rules subset subtree surface grammar syntax t₁ terminal string terminal symbol theorem theorem-proving theory transformational grammar transformational rules translation tree true truth-functionally unsatisfiable Turing machine undecidable v₁ variables vector x₁ Y₁ zero
Popular passages
Page 6 - An expression is either a term or a string of symbols consisting of a predicate symbol of degree ns 0 followed by n terms. A substitution component is any construct of the form v ->• t where v is a variable and t is a term different from v; v is called the variable of the substitution component v -> t and t is called the term (Hence v -+ v is not a substitution component for any variable v) . A substitution is a finite (possibly empty) set of substitution components with distinct lei'thand sides....