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We present a generic digit serial method (DSM) to compute the digits of a real number $V$ . Bounds on these digits, and on the errors in the associated estimates of $V$ formed from these digits, are derived. To illustrate our results, we derive such bounds for a parameterized family of high-radix algorithms for division and square root. These bounds enable a DSM designer to determine, for example, whether a given choice of parameters allows rapid formation and rounding of its approximation to $V$. All our claims are mechanically verified using the HOL-Light theorem prover, and are included in the appendix with commentary., 32 pages

We describe a HOL Light formalization of Hermite's proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover., Journal of Formalized Reasoning; Vol 4, No 1 (2011); 71-84

Perhaps the most difficult aspect of designing a shared memory multiprocessor is the hardware protocol that facilitates the sharing of memory by multiple processors; these protocols are thus a natural target for formal verification. In this thesis we consider several problems relevant to model checking these protocols. The ultimate specification of a protocol is the memory model. Our more theoretical contributions relate to the problem of model checking a protocol for the well-known memory model sequential consistency (SC). We define a restricted version of SC called decisive SC (DSC), which rules out pathologies admitted by SC, and explore the complexities of its verification problems. Our key results are that DSC of a single behavior is NP-complete, DSC of a protocol is PSPACE-hard, a bounded variant DSQ is decidable in EXPSPACE, and full SC remains undecidable even when we require protocol behaviors to be prefix-closed. Also, we show that SC in conjunction with the ubiquitous property data independence imply DSC, which is strong evidence that restricting attention to DSC will never preclude any real protocol. Our second area of contribution considers parameterized model checking (PMC) of protocols. Here the goal is algorithmic proof over all of the infinite configurations of a protocol family parameterized by one or more quantities. We develop a technique to automatically abstract a family parameterized by the number of addresses and the number of data values, such that (a subset of) SC of the abstraction implies that of the family. We apply this method successfully to two nontrivial protocols, and suggest user-assisted solutions if the abstraction blows up or is too coarse for successful verification. We also contribute an approach for sound and complete processor-PMC of state assertions. The approach uses BDD-based symbolic model checking, and harnesses the theory of well-structured transition systems (WSTS). WSTS disallow conjunctive guards, which are found in many protocols. To extend applicability, we provide an automatic reduction for systems with conjunctive guards. Experiments show the efficacy of our conjunctive guard reduction, and that our approach scales better with the local state of each processor when compared with the classical WSTS algorithm.

Therapy is inundated with self-report instruments/measures for clients (Corcoran & Fischer, 1987)(Touliatos, Perlmutter, & Straus, 1989); most of them focused for individual therapy. Many of these instruments are used for assessment purposes, while some others are related to outcome (Fredman & Sherman, 1987) (Corcoran & Fischer, 1987). One neglected area is that of instruments devised to measure satisfaction with specific content areas oftherapy. Another neglected area is an instrument designed specifically for marital/couple therapy. This research devised and tested a client self-report satisfaction measure specifically for couples in therapy. The items of the Marital Therapy Satisfaction Measure (MTSM) were derived from a review of literature of research focusing on both therapists' and clients' perspectives of important/essential elements linked to effective marital/couple therapy. Forty- five clients engaged in a minimum of four sessions of marital/couple therapy were surveyed. Clients completed the MTSM and the Oient Satisfaction Questionnaire (CSQ-8), a self-report satisfaction instrument with already established validity and reliability. Results reported a significant correlation between the MTSM and the CSQ-8. Further analysis on the data revealed gender and other demographic effects on levels of satisfaction with marital/couple therapy. Concerns regarding sample size and variance are discussed, as well as suggestions for furthering this research and the potential of the MTSM