2011/03/07 by Manfred Kufleitner, Kufleitner, Manfred, Alexander Lauser +1 · 1 citation
Computer Science · #68Q45 #F.4.1 #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #acm:68Q45 #cs.FL #cs.LO #msc:68Q45
paper · pdf · doi:10.48550/arxiv.1103.1353
arxiv created 2011/03/07 · arxiv updated 2015/03/18
The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of existential first-order logic without min- or max-predicate. For all fragments, we obtain effective algebraic characterizations. Moreover, we give new combinatorial proofs for the decidability of the membership problem for dot-depth 1/2 and dot-depth 1.