Introduction to Automata Theory, Languages, and Computation

Hopcroft, J. E., Ullman, J. D., & Computation, A. (1979). Introduction to Automata Theory, Languages, and Computation. Addison-Wesley.

Type

Book

Intellectual base

Textbook

Year

1979

Pages cited

1-9

Link

https://archive.org/details/introductiontoau0000hopc

Cited from

computer_science

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Computability
  • the limits of program-equivalence checking and program synthesis. Linguistics. The parsing problem for sufficiently general grammars (unrestricted phrase-structure grammars) is undecidable

    This sourceEstablishes that type-0 (unrestricted) phrase-structure grammars generate exactly the recursively enumerable languages and that their membership/recognition problem is undecidable — a structural reason general grammar parsing must use constrained classes.

• State and State Transition
  • The finite or infinite state space defining all possible conditions the system may occupy

Domain-specific

• Nested stack automaton
  • … and bottom markers, nested-store tree and active-stack rule, transition relation, create destroy and move operations, acceptance condition, determinism and recognized language class are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Pairing function
  • Cantor’s polynomial pairing is one primitive-recursive example; injective encodings, bijections and computably invertible pairings must be distinguished.
• Regular Grammar
  • The active nonterminal acts like a finite control state, which is why regular grammars and finite automata characterize the same class of string languages.

    This sourceThe text treats left- and right-regular grammars and the paired finite-automaton constructions.

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