The Ehrenfeucht conjecture: a compactness claim for finitely generated free monoids

Juhani Karhumäki
1984 Theoretical Computer Science  
We survey recent results on the so-called Ehrenfeucht Conjecture which states: For each language L over a finite alphabet z' there exists a finite subset F of f. such that for each pair (g, h) of morphisms on Z* the equation g(x) = h(x) holds for all x in L if and only if it holds for all x in F. We point out that the conjecture is closely related to the theory of equations in free monoids. We also state a surprising consequence of the conjecture: If it holds (even noneffectively) for al! DOL
more » ... nguages, then the HDOL sequence eql:ivalence problem is decidable. Furthermore. we give examples of when the con jecture is known to hold. In particular, we establish it fat all binary languages, as well as for all languages when attention is restricted to bounded delay morphisms of some fixed delay.
doi:10.1016/0304-3975(84)90004-5 fatcat:4vpzemym5zff7o2yrspf53vkyy