The first-order theory of linear one-step rewriting is undecidable
نویسندگان
چکیده
منابع مشابه
The First - Order Theory of Linear One - Step Rewritingis
The theory of one-step rewriting for a given rewrite system R and signature is the rst-order theory of the following structure: its universe consists of all-ground terms, and its only predicate is the relation \x rewrites to y in one step by R". The structure contains no function symbols and no equality. We show that there is no algorithm deciding the 9 8-fragment of this theory for an arbitrar...
متن کاملThe Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems
By reduction from the halting problem for Minsky’s two-register machines we prove that there is no algorithm capable of deciding the ∃∀∀∀-theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable ∃∀∗-theory of one step rewriting (strong undecidability). This improves...
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The recursive path orderings (short rpo) are orderings on terms introduced by N. Dershowitz. They are the most popular orderings used for proving the termination of term rewriting systems (see [4] for a survey). The reason for the usefulness of these orderings lies in their stability properties: if s > rpo t, then, for every context C, C[s] > rpo C[t] (this is the monotonicity property) and, as...
متن کاملThe Existential Fragment of the One-Step Parallel Rewriting Theory
It is known that the first-order theory with a single predicate → that denotes one-step rewriting reduction on terms is undecidable already for formulae with ∃∀ prefix. Several decidability results exist for the fragment of the theory in which the formulae start with the ∃ prefix only. This paper considers a similar fragment for a predicate → which denotes the parallel one-step rewriting reduct...
متن کاملOn the Theory of One-Step Rewriting in Trace Monoids
We prove that the first-order theory of the one-step rewriting relation associated with a trace rewriting system is decidable and give a nonelementary lower bound for the complexity. The decidability extends known results on semi-Thue systems but our proofs use new methods; these new methods yield the decidability of local properties expressed in first-order logic augmented by modulo-counting q...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00083-8