Previous investigations have sought to determine how listeners might locate word boundaries in the speech signal for the purpose of lexical access. Cutler (1990) proposes the Metrical Segmentation Strategy (MSS), such that only full vowels in stressed syllables and their preceding syllabic onsets are segmented from the speech stream. I report the results of several experiments which indicate that the listener segments the minimal word, a phonologically motivated prosodic constituent, during processing of the speech signal. These experiments were designed to contrast the MSS with two prosodic alternative hypotheses. The Syllable Hypothesis posits that listeners segment a linguistic syllable in its entirety as it is produced by the speaker. The Minimal Word Hypothesis proposes that a minimal word is segmented according to implicit knowledge the listener has concerning statistically probable characteristics of the lexicon. These competing hypotheses were tested by using a word spotting method similar to that in Cutler and Norris (1988). The subjects' task was to detect real monosyllabic words embedded initially in bisyllabic nonce strings. Both open (CV) and closed (CVC) words were embedded in strings containing a single intervocalic consonant. The prosodic constituency of this consonant was varied by manipulating factors affecting prosodic structure: stress, the sonority of the consonant, and the quality of the vowel in the first syllable. The assumption behind the method is that word detection will be facilitated when embedded word and segmentation boundaries are coincident. Results show that these factors are influential during segmentation. The degree of difficulty in word detection is a function of how well the speech signal corresponds to the minimal word. Findings are consistently counter to both the MSS and Syllable hypotheses. The Minimal Word Hypothesis takes advantage of statistical properties of the lexicon, ensuring a strategy which is successful more often than not. The minimal word specifies the smallest possible content word in a language in terms of prosodic structure while simultaneously affiliating the greatest amount of featural information within the structural limits. It therefore guarantees an efficient strategy with as few parses as possible.

Every knapsack problem may be relaxed to a cyclic group problem. In 1969, Gomory found the subadditive characterization of facets of the master cyclic group problem. We simplify the subadditive relations by the substitution of complementarities and discover a minimal representation of the subadditive polytope for the master cyclic group problem. By using the minimal representation, we characterize the vertices of cardinality length 3 and implement the shooting experiment from the natural interior point. The shooting from the natural interior point is a shooting from the inside of the plus level set of the subadditive polytope. It induces the shooting for the knapsack problem. From the shooting experiment for the knapsack problem we conclude that the most hit facet is the knapsack mixed integer cut which is the 2-fold lifting of a mixed integer cut. We develop a cutting plane algorithm augmenting cutting planes generated by shooting, and implement it on Wong-Coppersmith digraphs observing that only small number of cutting planes are enough to produce the optimal solution. We discuss a relaxation of shooting as a clue to quick shooting. A max flow model on covering space is shown to be equivalent to the dual of shooting linear programming problem.