Talk:Semi-Thue system

"Semi-"?

What does the prefix Semi mean here? Is there a Thue system that's non-semi? Semi means half. —The preceding unsigned comment was added by 15.251.169.70 (talk • contribs) .

A "Thue system" is a Semi-Thue system that is symmetric (either because for each X->Y you also have Y->X in the system, or because you define the system to allow applications of rules in both directions). Very often the term "Thue system" is also used for Semi-Thue system, as most interesting properties are very similar.--Stephan Schulz 20:27, 13 July 2006 (UTC)

What is it?

I read the article, but I still don't really understand what a Semi-Thue system is. Can someone de-jargonify and/or expand the the definition in the intro? Perhaps create a small example for the layman and explain how it differs from other string rewriting systems? Thanks. (I added a "cleanup-jargon" tag to the article for now.) -- HiEv 10:21, 8 October 2007 (UTC)

Obviously... ?

"Obviously R is a subset of ${\xrightarrow[{R}]{}}$. "

I would argue that it would be the other way around, i.e., that ${\xrightarrow[{R}]{}}\subset R$. The reason for that being the existence restriction on ${\xrightarrow[{R}]{}}$. Please confirm and correct, including the removal of "obvious", or, correct me here if I am missing something? 145.15.244.32 (talk) 18:50, 2 June 2017 (UTC)

To see that $R\subseteq {\xrightarrow[{R}]{}}$, take $x=y=\varepsilon$, $s=u$, and $t=v$ in the definition of ${\xrightarrow[{R}]{}}$. The typical case is that ${\xrightarrow[{R}]{}}$ relates infinitely many pairs of elements, and $R$ only finitely many. 130.243.94.123 (talk) 14:08, 6 September 2022 (UTC)

Quantum semi-Thue systems

The assertion that a quantum version of a semi-Thue system has to have all rules in both directions is dubious. The quantum requirement for reversibility (or unitarity, if one considers the operators acting on the quantum state) is that information is not destroyed, neither arbitrarily introduced, but a computation may still have distinguished forward and backward directions; going forward through a full adder quantum gate array is not the same as going backward through it. An assertion that the system is Thue rather comes very close to saying that every rewrite step has to be its own inverse, which seems to make it rather useless.

It would perhaps help if it was clarified how this quantum version of (semi-)Thue systems is supposed to deal with potential nondeterminism of the classical concept. 130.243.94.123 (talk) 14:36, 9 September 2022 (UTC)