On post correspondence problem for letter monotonic languages

Vesa Halava, Jarkko Kari, Yuri Matiyasevich
2009 Theoretical Computer Science  
We prove that for given morphisms g, h : {a 1 , a 2 , . . . , a n } → B * , it is decidable whether or not there exists a word w in the regular language a * 1 a * 2 · · · a * n such that g(w) = h(w). In other words, we prove that the Post Correspondence Problem is decidable if the solutions are restricted to be from this special language. This yields a nice example of an undecidable problem in integral matrices which cannot be directly proved undecidable using the traditional reduction from the Post Correspondence Problem.
doi:10.1016/j.tcs.2009.01.040 fatcat:b63hqkgmvzaq7k62aw35o2fife