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Following recent works connecting two-variable logic to circuits and monoids, we establish, for numerical predicate sets P satisfying a certain closure property, a one-to-one correspondence between F O[<, P]-uniform linear circuits, two-variable formulas with P predicates, and weak block products of monoids. In particular, we consider the case of linear TC… (More)

- Mark Mercer
- LATA
- 2008

We obtain several lower bounds on the language recognition power of Nayak's [12] generalized quantum finite automata (GQFA). Techniques for proving lower bounds on Kondacs and Watrous' one-way quantum finite automata (KWQFA) were introduced by Ambainis and Freivalds [2], and were expanded in a series of papers. We show that many of these techniques can be… (More)

In sequential decision making under uncertainty, as in many other modeling endeavors, researchers observe a dynamical system and collect data measuring its behavior over time. These data are often used to build models that explain relationships between the measured variables, and are eventually used for planning and control purposes. However, these… (More)

A particular problem with the release of dense nonaqueous phase liquids (DNAPLs) into the environment is identifying where the DNAPL is and if it is still moving. This question is particularly important at sites where thousands of cubic meters of DNAPLs were disposed of. To date, results from laboratory models have not been scaled to predict analogous… (More)

- Mark Mercer
- 2007

We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger's end-decisive model (which we call BPQFA) and a new QFA model (which we call LQFA) whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance… (More)

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