Book ChapterDOI
Inclusion is Undecidable for Pattern Languages
Tao Jiang,Arto Salomaa,Kai Salomaa,Sheng Yu +3 more
- pp 301-312
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TLDR
It is shown that inclusion is undecidable for (both erasing and nonerasing) pattern languages and that a special case of the inclusion problem, i.e., theclusion problem for terminal-free erasing pattern languages, is decidable.Abstract:
The inclusion problem for (nonerasing) pattern languages was raised by Angluin [1] in 1980. It has been open ever since. In this paper, we settle this open problem and show that inclusion is undecidable for (both erasing and nonerasing) pattern languages. In addition, we show that a special case of the inclusion problem, i.e., the inclusion problem for terminal-free erasing pattern languages, is decidable.read more
Citations
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Journal ArticleDOI
Incremental concept learning for bounded data mining
TL;DR: In this paper, a hierarchy of more and more powerful feedback learners in dependence on the number k of queries allowed to be asked is established, and the union of at most k pattern languages is shown to be iteratively inferable.
Book ChapterDOI
Finding Minimal Generalizations for Unions of Pattern Languages and Its Application to Inductive Inference from Positive Data
TL;DR: A syntactic notion of minimal multiple generalizations (mmg for short) is introduced to study the inferability of classes of unions of a bounded number of pattern languages to be polynomial time inferable from positive data.
Journal ArticleDOI
Characterizations of monotonic and dual monotonic language learning
TL;DR: These characterizations provide a unifying framework for learning from positive data under the various monotonicity constraints and yield additional insight into the problem of what a natural learning algorithm should look like.
Decision Problems for Pushdown Threads
TL;DR: In this article, the equivalence of pushdown threads is shown decidable whereas pushdown thread inclusion is undecidable, which is an example of a borderline crossing where equivalence problem is decidable, whereas the inclusion problem is not.
References
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Book
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TL;DR: This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.
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Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines
TL;DR: The main results of this paper show that the same notions of computability can be realized within the highly restricted monogenic formal systems called by Post the "Tag" systems, and within a peculiarly restricted variant of Turing machine which has two tapes, but can neither write on nor erase these tapes.
Journal ArticleDOI
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TL;DR: The main result is a polynomial-time algorithm for the special case of patterns containing only one variable symbol (possibly occurring several times in the pattern).
Journal ArticleDOI
Reversal-Bounded Multicounter Machines and Their Decision Problems
TL;DR: It is shown that the emptiness, infiniteness, dlsjointness, containment, universe, and equivalence problems are decidable for the class of deterministic two-way multlcounter machines whose input and counters are reversal-bounded.