Abstract
We study the connections between recognizable tree languages and rewrite systems. We investigate some decision problems. Particularly, let us consider the property (P): a rewrite system S is such that, for every recognizable tree language F, the set of S-normal forms of terms in F is recognizable too. We prove that the property (P) is undecidable. We prove that the existential fragment of the theory of ground term algebras modulo a congruence \(\mathop \leftrightarrow \limits^* E\) generated by a set E of equations such that there exists a finite, noetherian, confluent rewrite system S satisfying (P) with \(\mathop \leftrightarrow \limits^* S = \mathop \leftrightarrow \limits^* E\) is undecidable. Nevertheless, we develop a decision procedure for the validity of linear formulas in a fiagment of such a theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
