Factor oracle

Abstract: We introduce a new notion of weak factor recognition that is the foundation of new data structures and on-line string matching algorithms. We define a new automaton built on a string p = p1p2 ... pm that acts like an oracle on the set of factors pi ... pj. If a string is recognized by this automaton, it may be a factor of p. But, if it is rejected, it is surely not a factor. We call it factor oracle. More precisely, this automaton is acyclic, recognizes at least the factors of p, has m+ 1 states and a linear number of transitions. We give a very simple sequential construction algorithm to build it. Using this automaton, we design an efficient experimental on-line string matching algorithm (we conjecture its optimality in regard to the experimental results) that is really simple to implement. We also extend the factor oracle to predict that a string could be a suffix (i.e. in the set pi ... pm) of p. We obtain the suffix oracle, that enables in some cases a tricky improvement of the previous string matching algorithm.

Abstract: A system is described which uses the Audio Oracle algorithm for music analysis and machine improvisation. Some improvements on previous Factor Oracle-based systems are presented, including automatic model calibration based on measures from Music Information Dynamics, facilities for compositional structuring and automation, and an audio-based query mode which uses the input signal to influence the output of the generative system.

Abstract: A factor oracle is a data structure for weak factor recognition It is an automaton built on a string p of length m that is acyclic, recognizes at least all factors of p, has m+1 states which are all final, and has m to 2m-1 transitions In this paper, we give two alternative algorithms for its construction and prove the constructed automata to be equivalent to the automata constructed by the algorithms in [ACR01] Although these new O(m2) algorithms are practically inefficient compared to the O(m) algorithm given in [ACR01], they give more insight into factor oracles Our first algorithm constructs a factor oracle based on the suffixes of p in a way that is more intuitive Some of the crucial properties of factor oracles, which in [ACR01] need several lemmas to be proven, are immediately obvious Another important property however becomes less obvious A second algorithm gives a clear insight in the relationship between the trie or dawg recognizing the factors of p and the factor oracle recognizing a superset thereof We conjecture that an O(m) version of this trie-based algorithm exists