TY - JOUR
AU - Murwanashyaka, Juvenal
AB - 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.
TI - Hilbert’s tenth problem for term algebras with a substitution operator
JF - Computability
DO - 10.3233/com-230444
DA - 2024-11-28
UR - https://www.deepdyve.com/lp/ios-press/hilbert-s-tenth-problem-for-term-algebras-with-a-substitution-operator-0FcexJDfFQ
SP - 433
EP - 457
VL - 13
IS - 3-4
DP - DeepDyve
ER -