Problem
Research questions and friction points this paper is trying to address.
non-recursive trade-offs
two-way machines
descriptional complexity
finite automata
Non-recursive trade-offs for two-way machines
🤖 AI Summary
This study addresses the absence of recursive upper bounds on descriptive complexity growth in type conversions between two-way automata. Specifically, it investigates the non-recursive overhead incurred when converting a machine model A, capable of simulating linear counting automata, into another model B. By integrating techniques from computational complexity theory and formal language and automata theory, the analysis reveals that no recursive bound exists on the descriptive complexity of equivalent model transformations under specific computational capabilities. The primary contribution is a rigorous proof demonstrating that the growth in description size cannot be bounded by any recursive function in this setting. This result provides essential theoretical foundations for understanding the inherent complexity of automata equivalence transformations.
📝 Abstract
If the machines of some type A have enough resources to (i) solve problems that no machine of type B can solve, and (ii) simulate any unary two-way deterministic finite automaton that has access to a linearly-bounded counter, then typically no recursive function can upper bound the increase in the size of description when a machine of type A is replaced by an equivalent machine of type B.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Non-recursive trade-offs
Two-way machines
Descriptional complexity
Unary two-way deterministic finite automata
Linearly-bounded counter
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