## Mathematical Aspects of Computer ScienceJacob T. Schwartz, American Mathematical Society American Mathematical Soc., Dec 31, 1967 - 224 pages |

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### 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

algebra algorithm analysis applied assigned atoms automata theory automaton axioms bachelor base component binary calculation coefficients compiler complements complex symbol computation connected consider construct contains context-free grammar context-free languages corresponding cut-point decision problem defined denote derived phrase-marker elements equations equivalence example exists finite set flowchart G polynomials geometric given integers interpretation isolated cut-point iteration function latent clashes lemma lexical linear linguistics masks Math mathematical method natural languages node noun obtained operation perceptron phrase structure grammars phrase-marker polynomials predicate Predictive Analyzer probabilistic automata Proc procedure proof recursion regular events regular expressions result rewriting satisfy semantic definition semantic markers sentence sequence shown in Figure statement structural index subcategorization rules subset subtree surface grammar syntax terminal string terminal symbol theorem transformational grammar transformational rules translation tree true truth values truth-functionally unsatisfiable Turing machine undecidable variables vector verifiable

### Popular passages

Page 217 - REFERENCES (1) WW Bledsoe and I. Browning, "Pattern Recognition and Reading by Machine," 1959 Proceedings of the Eastern Joint Computer Conference, 225-232.

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....