Ambiguity and Communication
Juraj Hromkovic, Georg Schnitger

TL;DR
This paper investigates the ambiguity of nondeterministic finite automata (NFA), constructing language hierarchies based on ambiguity levels and demonstrating exponential size requirements for certain ambiguity constraints, thus resolving a long-standing open problem.
Contribution
It introduces a hierarchy for polynomial ambiguity in NFAs and proves exponential size lower bounds, solving a longstanding open problem in automata theory.
Findings
Established a hierarchy for polynomial ambiguity in NFAs.
Proved exponential size lower bounds for NFAs with restricted ambiguity.
Solved a long-standing open problem from Ravikumar and Ibarra (1989).
Abstract
The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with size k poly(r) and ambiguity O(nk), but Lr,k has only NFA's with exponential size, if ambiguity o(nk) is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998).
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression
