An algebraic characterization of frontier testable tree languages

Thomas Wilke
1996 Theoretical Computer Science  
The class of frontier testable (i.e., reverse definite) tree languages is characterized by a !inite set of pseudoidentities for tree algebras, which are introduced here for this characterization. An efficient algorithm is presented that decides whether a given tree automaton recognizes a frontier testable tree language. The algorithm runs in time O(mn3 + m*n*), where m is the cardinality of the alphabet and n is the number of states of the automaton. * *This is ofh called 'reverse deli&e', see
more » ... S] and [16]. 3 In the conference version of this paper [18], tree algebras were introduced as 'point-tree algebras'. 0304-3975/96/%09.50 @ 1996-Elsevier Science B.V. All rights reserved SSDI 0304-3975(95)00131-x Corresponding to Remark 5 we have the following. Remark 6. Let D be a finite tree algebra generated by DA and assume that the sets Ei with i 2 1 are defined as follows: Ei+l ={~~(a,q,q') 1 a E DA A(g,q') E CDT X Ei)U(Ei X&)) Then q E Ei if and only if there exists a homomorphism h: P + D such that h(Ti) = q.
doi:10.1016/0304-3975(95)00131-x fatcat:5nsyzhg4lbdfbgtwjfkwcknwlq