A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.Comment: 48 pages, 4 figures, RevTeX, one reference adde

Automated Reasoning over Deontic Action Logics with Finite Vocabularies

In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work. This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace parallel execution of actions and action complement, two action operators that may present difficulties in their treatment. One of the restrictions of this logic is that it uses vocabularies with a finite number of actions. In this article we prove that this restriction does not affect the coherence of the deduction system; in other words, we prove that the system is complete with respect to language extension. We also study the computational complexity of this extended deductive framework and we prove that the complexity of this system is in PSPACE, which is an improvement with respect to related systems.Comment: In Proceedings LAFM 2013, arXiv:1401.056

Refining SCJ Mission Specifications into Parallel Handler Designs

Safety-Critical Java (SCJ) is a recent technology that restricts the execution and memory model of Java in such a way that applications can be statically analysed and certified for their real-time properties and safe use of memory. Our interest is in the development of comprehensive and sound techniques for the formal specification, refinement, design, and implementation of SCJ programs, using a correct-by-construction approach. As part of this work, we present here an account of laws and patterns that are of general use for the refinement of SCJ mission specifications into designs of parallel handlers used in the SCJ programming paradigm. Our notation is a combination of languages from the Circus family, supporting state-rich reactive models with the addition of class objects and real-time properties. Our work is a first step to elicit laws of programming for SCJ and fits into a refinement strategy that we have developed previously to derive SCJ programs.Comment: In Proceedings Refine 2013, arXiv:1305.563

Process Algebras

Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems. They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems. Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external experiments

An instance of umbral methods in representation theory: the parking function module

We test the umbral methods introduced by Rota and Taylor within the theory of representation of symmetric group. We define a simple bijection between the set of all parking functions of length $n$ and the set of all noncrossing partitions of $\{1,2,...,n\}$. Then we give an umbral expression of the Frobenius characteristic of the parking function module introduced by Haiman that allows an explicit relation between this symmetric function and the volume polynomial of Pitman and Stanley