Windable Heads & Recognizing NL with Constant Randomness

M. Utkan Gezer

doi:10.1007/978-3-030-40608-0_12

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arXiv · 1912.01382

Windable Heads & Recognizing NL with Constant Randomness

M. Utkan Gezer

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Abstract

Every language in NL has a $k$-head two-way nondeterministic finite automaton (2nfa($k$)) recognizing it. It is known how to build a constant-space verifier algorithm from a 2nfa($k$) for the same language with constant-randomness, but with error probability $\tfrac{k^2-1}{2k^2}$ that can not be reduced further by repetition. We have defined the unpleasant characteristic of the heads that causes the high error as the property of being "windable". With a tweak on the previous verification algorithm, the error is improved to $\tfrac{k_{\textrm{W}}^2-1}{2k_{\textrm{W}}^2}$, where $k_{\textrm{W}} \le k$ is the number of windable heads. Using this new algorithm, a subset of languages in NL that have a 2nfa($k$) recognizer with $k_{\textrm{W}} \le 1$ can be verified with arbitrarily reducible error using constant space and randomness.

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BibTeX RIS

M. Utkan Gezer. 2019-12-03. Windable Heads & Recognizing NL with Constant Randomness. https://doi.org/10.1007/978-3-030-40608-0_12

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