Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator

Juvenal Murwanashyaka

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arXiv · 2111.00573

Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator

Juvenal Murwanashyaka

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Abstract

We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction of Post`s Correspondence Problem. By a different method, we show that deciding truth of sentences with one existential quantifier and one bounded universal quantifier is undecidable.

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BibTeX RIS

Juvenal Murwanashyaka. 2021-10-31. Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator. https://arxiv.org/abs/2111.00573

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