Affiliations: [a] Department of Computer Science, The University of Prince Edward Island, Charlottetown, PE, Canada. ccampeanu@upei.ca | [b] Centro de Matemática e Faculdade de Ciências da Universidade do Porto, 4169-007 Porto, Portugal. nam@dcc.fc.up.pt, rvr@dcc.fc.up.pt
Correspondence:
[*]
Address for correspondence: Department of Computer Science, The University of Prince Edward Island, Charlottetown, PE, Canada
Note: [†] This work was partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under projects PEst-C/MAT/UI0144/2013 and FCOMP-01-0124-FEDER-020486.
Abstract: Given a language L, we study the language of words D(L), that distinguish between pairs of different left quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from closure operators and Boolean operators. For the case of regular languages, we give an upper bound for the state complexity of the distinguishability operation, and prove its tightness. We show that the set of minimal words that can be used to distinguish between different left quotients of a regular language L has at most n – 1 elements, where n is the state complexity of L, and we also study the properties of its iteration. We generalize the results for the languages of words that distinguish between pairs of different right quotients and two-sided quotients of a language L.
Keywords: Formal Languages, Myhill-Nerode Relations, Quotients, Language Operations, Closures, Regular Languages, State Complexity
