%0 Conference Paper
%B CALCO - 5th Conference on Algebra and Coalgebra in Computer Science
%D 2013
%T A coalgebraic view of e- transitions
%A Alexandra Silva
%A Bram Westerbaan
%C Warsaw, Poland
%I Springer
%V 8089
%X <p>In automata theory, a machine transitions from one state to the next when it reads an input symbol. It is common to also allow an automaton to transition without input, via an ε-transition. These ε-transitions are convenient, e.g., when one defines the composition of automata. However, they are not necessary, and can be eliminated. Such ε-elimination procedures have been studied separately for different types of automata, including non-deterministic and weighted automata.<br /> It has been noted by Hasuo that it is possible to give a coalgebraic account of ε-elimination for some automata using trace semantics (as defined by Hasuo, Jacobs and Sokolova).<br /> In this paper, we give a detailed description of the ε-elimination procedure via trace semantics (missing in the literature). We apply this framework to several types of automata, and explore its boundary.<br /> In particular, we show that is possible (by careful choice of a monad) to define an ε-removal procedure for all weighted automata over the positive reals (and certain other semirings). Our definition extends the recent proposals by Sakarovitch and Lombardy for these semirings.</p>
%8 September
%> https://haslab.uminho.pt/sites/default/files/xana/files/main.pdf