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Joined 2026-09-21 Message
Incoming links: John Hopcroft
John Hopcroft 2026-11-05
John Hopcroft gave a 1971 algorithm for minimizing deterministic finite automata with running time for states and alphabet . It refines partitions of states until states in the same block accept exactly the same continuation strings.[ref]
An n log n Algorithm for Minimizing States in a Finite Automaton by John Hopcroft. Introduction and Analysis of the running time
The key accounting idea is to organize refinement around smaller splitters. A transition can then be charged to only logarithmically many successively smaller blocks, instead of rescanning every state in every refinement round. DFA minimization preserves the recognized language while merging observationally equivalent states, making representation size and equivalence checking algorithmic questions.
John Hopcroft, portrait published by Cornell University
. Seymour Ginsburg 2026-11-05
Seymour Ginsburg coauthored the 1969 studies of the abstract family of languages framework with Sheila Greibach and John Hopcroft. This approach compares formal-language classes through closure properties instead of one particular grammar or machine presentation.[ref]
Studies in Abstract Families of Languages by Seymour Ginsburg and others. Abstract families of languages, pp.1–32
For example, closure under intersection with regular languages permits restricting an existing language by a finite-state filter. That property is weaker than closure under arbitrary intersections: two context-free languages can have a non-context-free intersection. Stating the allowed operation precisely keeps a shared abstract framework from incorrectly identifying different language classes.
Sheila Greibach 2026-11-05
Sheila Greibach coauthored the 1969 work on the abstract family of languages framework with Seymour Ginsburg and John Hopcroft. Their framework separates common language operations from the particular recognizers used to implement them.[ref]
Studies in Abstract Families of Languages by Seymour Ginsburg and others. Abstract families of languages, pp.1–32; collection byline
One important distinction is between nonerasing word homomorphisms and arbitrary word homomorphisms. Allowing an alphabet symbol to map to the empty word can discard arbitrarily much of a derivation's written evidence. A full abstract family of languages allows that operation, while the ordinary framework only requires the nonerasing version. The distinction prevents an apparently small change in a closure axiom from concealing a substantive change of computational behavior.