Rewriting preserving recognizability of finite tree languages

Layered Transducing Term Rewriting System and Its Recognizability Preserving Property

A term rewriting system which effectively preserves recognizability (EPR-TRS) has good mathematical properties. In this paper, a new subclass of TRSs, layered transducing TRSs (LT-TRSs) is defined and its recognizability preserving property is discussed. The class of LT-TRSs contains some EPRTRSs, e.g., {f(x) → f(g(x))} which do not belong to any of the known decidable subclasses of EPR-TRSs. B...

Left-linear Bounded TRSs are Inverse Recognizability Preserving

Bounded rewriting for linear term rewriting systems has been defined in (I. Durand, G. Sénizergues, M. Sylvestre. Termination of linear bounded term rewriting systems. Proceedings of the 21st International Conference on Rewriting Techniques and Applications) as a restriction of the usual notion of rewriting. We extend here this notion to the whole class of left-linear term rewriting systems, an...

On transformations of formal power series

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, ge...

Recognizing Boolean Closed A-Tree Languages with Membership Conditional Rewriting Mechanism

This paper provides an algorithm to compute the complement of tree languages recognizable with A-TA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizability of A-closures of regular tree languages. In the proof of the main result, a new framework of tree aut...

Bottom-Up Rewriting Is Inverse Recognizability Preserving