## 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 assume atoms automata base calculation called clash clauses command complex component computation condition connected consider consists construct contains context-free languages corresponding Count defined definition denote derived described determine effect elements equations equivalence example exists expressions fact Figure finite function given gives grammar Hence initial input interesting interpretation languages lexical linear linguistics machine markers Math mathematical means method natural node Note obtained operation particular phrase phrase-marker polynomials positive possible predicate present problem procedure proof prove question recursion regular relation represented result rules satisfy semantic sentence sequence shown simple statement step string structure subset surface symbol syntactic terminal theorem theory transformational transformational grammar translation tree true variables zero

### 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....