Finite-valued distance automata

Finite-Valued Weighted Automata

Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defi...

Characterizations of complete residuated lattice-valued finite tree automata

This paper deals with the concept of complete residuated lattice-valued (referred to as L-valued) finite tree automata. In this regard, we first define an L-valued regular tree language, and then we prove a necessary and sufficient condition for the regularity of an L-valued tree language. Furthermore, we generalize the pumping lemma for L-valued finite tree automata (L-FTA). Afterwards, the be...

Multidimensional fuzzy finite tree automata

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

Finite Automata

• F ⊆ Q is the set of accept or final states. The behavior of a DFA M on an input string x ∈ Σ∗ is as follows. It reads the symbols in x one at a time, from left to right. At each point in time, the automaton has a current state. Initially, the automaton is in state s. If the current state of the automaton is q, and the next symbol in x to be read is a, then the automaton on reading a transitio...

Finite Automata