The factor oracle is a relatively new data structure for the set of factors of a string. It has been introduced by Allauzen, Crochemore, and Raffinot in 1999. It may recognize nonfactors (hence the name “oracle”) but its implementational simplicity and experimental behaviour are stunning; factor oracle based string matching has been conjectured optimal on average. However, its structure is not ...

The partial derivative automaton (Apd) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic...

We present a technique for reachability analysis of continuous multi-affine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multiaffine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evalua...

Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT). The AT automaton has two quotients discussed: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT, the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the partia...

The goal of this paper is to identify a more efficient algorithm for the computation of the path of minimum ratio (i.e. the quotient of the weight divided by the length) in a weighted graph. The main application of this technique is to improve the efficiency of reachability analysis for flat counter automata with Difference Bound Matrix constraints on transitions. A previous result showed that ...

We explore the combinatorial properties of the branching areas of paths in higher dimensional automata. Mathematically, this means that we investigate the combinatorics of the negative corner homology of a globular ω-category and the combinatorics of a new homology theory called the reduced negative corner homology. This latter is the homology of the quotient of the corner complex by the sub-co...

The intention of the present study is to establish general framework for automated problem solving by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with gluing forms connecting inand out-edges to nodes. Nets are caused to undergo transformations in conceptual level by type wise differentiated intervening net rew...

Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT ). The AT automaton has two quotients considered: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT , the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the par...