Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas

This flyer promotes the event "A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas", part at the SIPA at Books & Books series. This event held at Books & Books in Coral Gables.

Development of the Sphere Overlap Scale (SOS) : compartmentalization and the spillover hypothesis

The purpose of this study was to create a scale that could measure compartmentalization. In the first of two studies 311 working undergraduates were asked to indicate agreement with 119 items that measured compartmentalization. The resulting scale's reliability and validity were evaluated by having a second sample of 312 working students complete the items that comprise a sphere overlap scale, two measures of spillover, and a measure of personality, coping, and demoralization. Although the study's original goal was not realized, its procedures were successful in developing a short (10-item) measure of work-to-home spillover whose items loaded on a single factor. Structural equation modeling indicated that SOS items were correlated with existing measures of spillover and could be discriminated from related concepts of personality and coping. The SOS was also more highly correlated with demoralization than existing measures of spillover in hierarchical analyses that controlled for demographic factors, personality characteristics, and coping style. It is concluded that the SOS shows enough promise to warrant the cost of its appraisal as an alternative measure of spillover in a longitudinal study.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Examination of the overlap between DSM-111-R overanxious disorder and DSM-IV generalized anxiety disorder in childhood

Since DSM-III-R criteria for Overanxious Disorder (OAD) was subsumed under Generalized Anxiety Disorder (GAD) in DSM-IV, three studies have investigated the overlap between the diagnoses. Although two studies have identified children meeting both OAD and GAD criteria (OAD/GAD group), a third study has identified children who met criteria for OAD, but not GAD (OAD group). Based on finding these two groups of children, we examined whether children in the OAD group (n= 30) could be differentiated from children in the OAD/GAD group (n=81) based on self and parent report of anxious symptoms and level of functional impairment. Conditional probability rates were also calculated for each of the DSM anxious symptoms to determine their overall clinicalutility. Findings revealed that the OAD group of children experienced fewer anxious symptoms than children in the OAD/GAD group, though both groups showed some amount of impairment. The implications for research and practice are discussed.