Follow automata

An Efficient Coq Tactic for Deciding Kleene Algebras

“…At first, we implemented Thompson's construction [36], for its simplicity; we finally switched to a variant of the Ilie and Yu's construction [19] which produces smaller automata. This algorithm constructs an automaton with a single initial state and a single accepting state (respectively denoted by i and f ); it proceeds by structural induction on the given regular expression.…”

“…3.2) was inspired by the standard notion of star normal form [8] and the idea of star unavoidability [19]. To our knowledge, the facts that we can always rewrite regular expressions in such a form and that -NFAs with acyclic epsilon-transitions can be constructed in this way are new.…”

Prefix and Right-Partial Derivative Automata

“…The standard conversion with ε-transitions is the Thompson automaton (A T ) [15] and the standard conversion without ε-transitions is the Glushkov (or position) automaton (A pos ) [9]. Other conversions such as partial derivative automaton (A pd ) [1,13] or follow automaton (A f ) [10] were proved to be quotients of the A pos , by specific right-invariant equivalence relations [6,10]. In particular, for REs under special conditions, A pd is an optimal conversion method [12].…”

Multi-Tilde-Bar Derivatives

“…Antimirov derivatives have been recently extended to unrestricted regular expressions [10]; extended partial derivatives are sets of sets of expressions and they provide a DFA, a NFA and an AFA (alternating finite automaton) [11]. Some derivations are based on the linearization of the (simple) input expression: let us cite the continuations of Berry and Sethi [4], the c-continuations of Champarnaud and Ziadi [14] and the derivatives of Ilie and Yu [18]. Let us mention that Antimirov derivation has been extended to the case of weighted rational expressions [21,13].…”