Universit a Di Pisa from String Rewriting to Logical Metabolic Systems from String Rewriting to Logical Metabolic Systems

Termination of Cycle Rewriting by Transformation and Matrix Interpretation

We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. We present three such transformations, and prove for all of them that ...

String Rewriting and Metabolism: a Logical Perspective

Lynch-Morawska Systems on Strings

We investigate properties of convergent and forward-closed string rewriting systems in the context of the syntactic criteria introduced in [8] by Christopher Lynch and Barbara Morawska (we call these LM-Systems). Since a string rewriting system can be viewed as a term-rewriting system over a signature of purely monadic function symbols, we adapt their definition to the string rewriting case. We...

Parsing and Generation as Datalog Queries

We show that the problems of parsing and surface realization for grammar formalisms with “context-free” derivations, coupled with Montague semantics (under a certain restriction) can be reduced in a uniform way to Datalog query evaluation. As well as giving a polynomialtime algorithm for computing all derivation trees (in the form of a shared forest) from an input string or input logical form, ...

Undecidable Properties on Length-Two String Rewriting Systems

Length-two string rewriting systems are length preserving string rewriting systems that consist of length-two rules. This paper shows that confluence, termination, left-most termination and right-most termination are undecidable properties for length-two string rewriting systems. This results mean that these properties are undecidable for the class of linear term rewriting systems in which dept...