On The Liniar Time Complexity of Finite Languages
Mircea Alexandru Popescu Moscu
TL;DR
This paper proves that for any finite language, there exists a Turing machine that recognizes it within a linear time bound of at most input length plus one, establishing a clear time complexity result.
Contribution
It introduces a formal proof that finite languages can be recognized by Turing machines within linear time, specifically at most input length plus one steps.
Findings
Finite languages can be recognized in linear time.
Turing machines can decide finite languages within at most k+1 steps for input length k.
The paper establishes a formal bound on the time complexity for finite languages.
Abstract
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing machine that computes the language in such a way that for any input of length k the machine stops in, at most, k + 1 steps.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic