## Paper: Monadic theory of term rewritings (at LICS 1992)

Authors:**Caucal, D.**

### Abstract

The monadic second-order theory of term rewritings is considered. It is shown that the monadic theory of the rewriting (or the suffix rewriting) of a ground rewrite system is undecidable. Furthermore, the first-order theory is undecidable for the prefix derivation according to a linear context-free grammar on linear terms. Nevertheless, a new notion on terms with variables is introduced: a term is entire if each of its subterms either is a variable, or is without variable or has the same variables as the term. It is shown that the monadic theory is decidable (respectively undecidable) for the prefix rewriting according to a rewrite system on entire terms, with an axiom (respectively without axiom)

### BibTeX

@InProceedings{Caucal-Monadictheoryofterm, author = {Caucal, D.}, title = {Monadic theory of term rewritings}, booktitle = {Proceedings of the Seventh Annual IEEE Symp. on Logic in Computer Science, {LICS} 1992}, year = 1992, editor = {Andre Scedrov}, month = {June}, pages = {266--273}, location = {Santa Cruz, CA, USA}, publisher = {IEEE Computer Society Press} }