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The intersection problem for alphabetic vector monoids. (English) Zbl 0883.68077
Summary: Let $$\Sigma$$ and $$\Gamma$$ be two vector alphabets consisting of alphabetic vectors $$(a_1,a_2)$$, where $$a_1,a_2\in A\cup \{\varepsilon\}$$ for an alphabet $$A$$. We show that it is decidable whether or not $$\Sigma^\otimes \cap \Gamma^\otimes$$ is the trivial submonoid of the direct product $$A^* \times A^*$$ for the generated submonoids $$\Sigma^\otimes$$ and $$\Gamma^\otimes$$. On the other hand we show that a simple version, obtained from letter-to-letter homomorphisms, of the modified Post Correspondence Problem is undecidable for alphabetic vectors.
##### MSC:
 68Q45 Formal languages and automata
##### Keywords:
alphabetic vectors
Full Text:
##### References:
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