Backward and forward bisimulation minimization of tree automata

Efficient Implementation for Deterministic Finite Tree Automata Minimization

“…In this paper, we present an efficient implementation of DFTA using usual graph properties. We give a general algorithm for the standard minimization and we show that the asymptotic complexity of this construction reaches the best known one which can be deduced by combining Abdullah et al [18] and Högberg et al [20] works on NFTA. For the second, we extend materials presented in [21] and we detail a new incremental DFTA minimization approach.…”

“…But, Abdullah et al [18] introduced a method in which they adapted Paige-Tarjan algorithm [19] to refine an equivalence relation in order to minimize a non-deterministic automata (NFTA). Since the deterministic automata is a particular case of non-deterministic automata, the last approach works well for it and gives the best known complexity in tree case which is O(r⋅m⋅log(n)) where r is the maximum rank of the alphabet, m is the size of the automaton and n is the number of its states (see [20]). In this paper, we present an efficient implementation of DFTA using usual graph properties.…”

Hyper-Minimization for Deterministic Tree Automata

“…It is well-known that M is minimal if and only if it does not have two dierent, but equivalent states. For every dta M , an equivalent minimal dta can be computed eciently using an adaptation [7] of Hopcroft's algorithm [9], which runs in time O( m log n) where = max rk(Σ) is the maximal rank of the input symbols, m = |dom(δ)| is the number of transitions, and n = |Q| is the number of states. From now on, let M = (Q, Σ, δ, F ) be a minimal dta, which automatically yields that M is trim.…”

“…Thus, our hyper-minimization for dta is based on a congruence that is similar to the context-language equivalence used in dta minimization [3]. The fastest known algorithm for dta minimization [7] runs in time O( m log n), where is the maximal rank of the input symbols, m is the number of transitions, and n is the number of states of the input dta. The hyper-minimization algorithm that we present has the run-time complexity O( mn), which is slightly worse than traditional minimization, but we believe that our algorithm can be improved using the standard techniques used in hyper-minimization of dfa.…”

Learning Rational Functions

“…Learning algorithms for regular languages of words or trees are usually based on the Myhill-Nerode theorem, that is on an algebraic characterization of the unique minimal automaton recognizing the target language [14,2,6,13]. The learning problem is then to identify this unique automaton in the limit from finite samples of positive and negative examples that characterize the language.…”