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- Argimiro Arratia, Carlos E. Ortiz
- LATIN
- 2004

We present a probability logic (essentially a first order language extended with quantifiers that count the fraction of elements in a model that satisfy a first order formula) which, on the one hand, captures uniform circuit classes such as AC 0 and TC 0 over arithmetic models, namely, finite structures with linear order and arithmetic relations, and, on… (More)

- Argimiro Arratia, Carlos E. Ortiz
- J. Log. Comput.
- 2006

We present a second order logic of proportional quantifiers, SOLP, which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r–tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different… (More)

- Argimiro Arratia, Carlos E. Ortiz
- Electronic Colloquium on Computational Complexity
- 2006

We formulate a formal syntax of approximate formulas for the logic with counting quantifiers, SOLP, studied by us in [1], where we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation to an almost order (in… (More)

- Argimiro Arratia, Carlos E. Ortiz
- LATIN
- 2006

We present a second order logic of proportional quantifiers, , which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r– tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different… (More)

- Argimiro Arratia, Carlos E. Ortiz
- WoLLIC
- 2013

The first order logic Ring(0, +, * , <) for finite residue class rings with order is presented, and extensions of this logic with generalized quantifiers are given. It is shown that this logic and its extensions capture DLOGT IM E-uniform circuit complexity classes ranging from AC 0 to T C 0. Separability results are obtained for the hierarchy of these… (More)

- Carlos Eduardo Cuadros Ortiz, Dushan Boroyevich, +4 authors William Baumann
- 2003

ZVZCS full-bridge converters, soft-switched three-phase buck rectifier, space vector modulation. ABSTRACT A systematic and versatile method to derive accurate and efficient Circuit Oriented Large Signal Average Models (COLSAMs) that approximate the slow dynamics manifold of the moving average values of the relevant state variables for Pulse-Width Modulated… (More)

- Argimiro Arratia, Carlos E. Ortiz
- ArXiv
- 2015

Separations among the first order logic Ring(0, +, *) of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study… (More)

- Argimiro Arratia, Carlos E. Ortiz
- Logic Journal of the IGPL
- 2009

This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and some of its fragments capture the classes P and NL; (ii)… (More)

- Carlos E. Ortiz
- 2008

We prove a Model Existence Theorem for a fully infinitary logic L A for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson ([7]) and studied in different forms by Anderson ([1]) and Fajardo and Keisler ([2]). This theorem extends Henson's… (More)

We present a formal syntax of approximate formulas suited for the logic with counting quantifiers SOLP. This logic was studied by us in [1] where, among other properties, we showed: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation… (More)