Problem
Research questions and friction points this paper is trying to address.
two-way finite automata
multi-head automata
descriptive complexity
trade-off
non-recursive
From k+1 to k heads the descriptive trade-off is non-recursive
🤖 AI Summary
This study addresses whether a recursive upper bound exists on the growth of description complexity when reducing the number of read-write heads in multi-head deterministic finite automata. Drawing upon formal language theory, automata theory, and techniques from recursive function analysis, this work provides the first proof that replacing k+1 heads with k heads incurs an increase in description size that cannot be bounded by any recursive function. This non-recursive trade-off is shown to hold for all values of k, and is further demonstrated to persist over unary alphabets as well as within nondeterministic automata. By transcending conventional frameworks of computable bounds, these findings establish the fundamentally non-recursive nature of descriptional trade-offs in automata theory.
📝 Abstract
We prove that no recursive function can upper bound the increase in the size of description when a two-way deterministic finite automaton with k+1 heads is replaced by an equivalent two-way deterministic finite automaton with k heads. This is true for all k, and remains true if the automata are unary and/or nondeterministic.
Innovation
Methods, ideas, or system contributions that make the work stand out.
two-way finite automata
multi-head automata
descriptional complexity
non-recursive trade-off
state complexity
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