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Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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NFA Minimization is a problem: Given an NFA A, find an equivalent NFA A' (i.e., L(A') = L(A)) with the
minimum number of states. Show that if NFA Minimization could be solved in deterministic polytime, then
P = NP.
Hint: For a 3-CNF formula (₁,...,n) with m clauses, show how to construct in polytime an NFA with O(nm)
states that accepts all nonsatisfying assignments of p, represented as boolean strings of length n.
Transcribed Image Text:NFA Minimization is a problem: Given an NFA A, find an equivalent NFA A' (i.e., L(A') = L(A)) with the minimum number of states. Show that if NFA Minimization could be solved in deterministic polytime, then P = NP. Hint: For a 3-CNF formula (₁,...,n) with m clauses, show how to construct in polytime an NFA with O(nm) states that accepts all nonsatisfying assignments of p, represented as boolean strings of length n.
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