Locally threshold testable languages in strict sense: Application to the inference problem
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The aim of this paper is to define a new family of regular languages, the Locally Threshold Testable Languages in Strict Sense (LTTSS). This family includes the well known family of locally testable languages in strict sense (LTSS) and is included in the family of locally threshold testable languages (LTT). Membership of a word to a LTTSS language can be decided by means of local scanning, using a sliding window of a fixed length k, although in this case, we have to care that the number of occurrences of certain segments of length ≤ k in the words is not greater than a level of restriction, less than a threshold r. As LTTSS languages may be of interest in disciplines such as Pattern Recognition and specially in Speech Recognition, an inference algorithm that identifies the family of (k,r)-TTSS languages from positive data in the limit is proposed. Finally we also report some results aiming to reflect the evolution of the behavior of this algorithm for different values of k and r when it is used in a handwritten digits recognition task.
KeywordsSpeech Recognition Strict Sense Locally Testable Regular Language Positive Data
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