Hilbert’s Tenth Problem for Term Algebras with a Substitution Operator

Murwanashyaka, Juvenal

doi:10.1007/978-3-031-08740-0_17

Lecture Notes in Computer Science

2022

DOI: 10.1007/978-3-031-08740-0_17

|View full text |Cite

Hilbert’s Tenth Problem for Term Algebras with a Substitution Operator

Juvenal Murwanashyaka

Abstract: We introduce a first-order theory of finite full binary trees and show that the analogue of Hilbert's Tenth Problem is undecidable by constructing a many-to-one reduction of Post's Correspondence Problem.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Hilbert’s tenth problem for term algebras with a substitution operator

Murwanashyaka

2024

COM

View full text Add to dashboard Cite

The analogue of Hilbert’s 10th Problem for a first-order structure A with signature L asks whether there exists an algorithm that given an L-sentence of the form ∃ x → [ s = t ] decides whether ∃ x → [ s = t ] is true in A. In this paper, we consider term algebras over a finite signature with at least one constant symbol and one function symbol of arity at least two. We investigate the structure we obtain by extending the term algebra with a substitution operator. We prove undecidability of the analogue of Hilbert’s 10th problem without relying on the solution to the original Hilbert’s 10th Problem.

show abstract

Hilbert’s tenth problem for term algebras with a substitution operator

Murwanashyaka

2024

COM

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Hilbert’s Tenth Problem for Term Algebras with a Substitution Operator

Abstract: We introduce a first-order theory of finite full binary trees and show that the analogue of Hilbert's Tenth Problem is undecidable by constructing a many-to-one reduction of Post's Correspondence Problem.

Cited by 1 publication

References 5 publications

Hilbert’s tenth problem for term algebras with a substitution operator

Hilbert’s tenth problem for term algebras with a substitution operator

Contact Info

Product

Resources

About