Computer Science > Formal Languages and Automata Theory
[Submitted on 19 Sep 2022 (v1), last revised 7 Nov 2024 (this version, v6)]
Title:Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages
View PDFAbstract:A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning algorithm $\textbf{L}$ returns a hypothesis equivalent to $L$. Which omega automata have characteristic sets of polynomial size, and can these sets be constructed in polynomial time? We address these questions here. In brief, non-deterministic omega automata of any of the common types, in particular Büchi, do not have characteristic samples of polynomial size. For deterministic omega automata that are isomorphic to their right congruence automata, the fully informative languages, polynomial time algorithms for constructing characteristic samples and learning from them are given. The algorithms for constructing characteristic sets in polynomial time for the different omega automata (of types Büchi, coBüchi, parity, Rabin, Street, or Muller), require deterministic polynomial time algorithms for (1) equivalence of the respective omega automata, and (2) testing membership of the language of the automaton in the informative classes, which we provide.
Submission history
From: Dana Fisman [view email] [via LMCS proxy][v1] Mon, 19 Sep 2022 20:36:12 UTC (1,011 KB)
[v2] Fri, 15 Sep 2023 14:35:54 UTC (68 KB)
[v3] Mon, 22 Apr 2024 08:30:29 UTC (76 KB)
[v4] Sun, 11 Aug 2024 20:06:07 UTC (74 KB)
[v5] Sat, 31 Aug 2024 16:48:38 UTC (100 KB)
[v6] Thu, 7 Nov 2024 10:04:48 UTC (101 KB)
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