Introduction to Automata Theory, Languages, and Computation¶

Hopcroft, J. E., Motwani, R., & Ullman, J. D. (2006). Introduction to Automata Theory, Languages, and Computation. Pearson.

Type: Book chapter
Intellectual base: Textbook
Year: 2006
Link: https://archive.org/details/trent_0116301269779
Cited from: computer_science, linguistics_semiotics, mathematics

Cited by¶

7 citations across 7 artifacts.

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

Primes¶

Closure
- The regular languages are closed under union, intersection, complement, concatenation, Kleene star, reversal, and homomorphism — the strong closure properties make regular languages the canonical "well-behaved" class of formal languages, and many algorithmic results in compiler design and string processing rely on these closures, as Hopcroft, Motwani, and Ullman (2006) catalogue in their canonical automata-theory textbook.
  This sourceStandard automata-theory text cataloguing the closure-properties profiles of regular, context-free, and recursively-enumerable language classes.
Local Sequence Legality
- Formal grammars and parsing: regular expressions, context-free grammars, and programming-language tokenisation, where legality is decided before semantic analysis.
  This sourceRegular versus context-free languages; the pumping lemma showing a regular grammar cannot match balanced parentheses at arbitrary depth.
Rule of Least Power (Minimum Sufficient Capability)
- The power-ordered mechanism space is the Chomsky hierarchy: regular expressions below context-free grammars below Turing-complete code.
  This sourceStandard reference for the Chomsky hierarchy (regular ⊂ context-free ⊂ recursively enumerable) and the guaranteed linear-time, halting behavior of finite automata.

Domain-specific¶

Deterministic Finite Automaton
- Because each state-symbol pair has exactly one successor, the run is unique; the word is accepted precisely when that run ends in F.
Emptiness problem
- Emptiness problem is a decision problem asking whether the language denoted by a given formal representation contains no valid strings.
Formal Language
- This language–presentation separation is what makes closure, equivalence, expressiveness, decidability, and complexity questions precise.
Regular Grammar
- Textbooks differ about whether unit productions, empty productions, multi-terminal (w), or only \(S\to\varepsilon\) are admitted, so a rigorous use must state its convention.
  This sourceExercise 5.1.4 gives the extended right-linear forms \(A\to wB\) and \(A\to w\) and the automaton equivalence.

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