1,100 research outputs found
Modular Construction of Complete Coalgebraic Logics
We present a modular approach to defining logics for a wide variety of state-based systems. The systems are modelled by coalgebras, and we use modal logics to specify their observable properties. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular fashion. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems, for which no complete axiomatisation has been obtained so far
Binary Reachability of Timed Pushdown Automata via Quantifier Elimination and Cyclic Order Atoms
We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an integer sort. This subsumes analogous expressibility results previously known for finite and pushdown timed automata with untimed stack. As key technical tools, we use quantifier elimination for a fragment of hybrid linear arithmetic and for cyclic order atoms, and a reduction to register pushdown automata over cyclic order atoms
Disjunctive bases: normal forms and model theory for modal logics
We present the concept of a disjunctive basis as a generic framework for
normal forms in modal logic based on coalgebra. Disjunctive bases were defined
in previous work on completeness for modal fixpoint logics, where they played a
central role in the proof of a generic completeness theorem for coalgebraic
mu-calculi. Believing the concept has a much wider significance, here we
investigate it more thoroughly in its own right. We show that the presence of a
disjunctive basis at the "one-step" level entails a number of good properties
for a coalgebraic mu-calculus, in particular, a simulation theorem showing that
every alternating automaton can be transformed into an equivalent
nondeterministic one. Based on this, we prove a Lyndon theorem for the full
fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform
Interpolation result, for both the full mu-calculus and its fixpoint-free
fragment, and a Janin-Walukiewicz-style characterization theorem for the
mu-calculus under slightly stronger assumptions.
We also raise the questions, when a disjunctive basis exists, and how
disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla
formulas provide disjunctive bases for many coalgebraic modal logics, but there
are cases where disjunctive bases give useful normal forms even when nabla
formulas fail to do so, our prime example being graded modal logic. We also
show that disjunctive bases are preserved by forming sums, products and
compositions of coalgebraic modal logics, providing tools for modular
construction of modal logics admitting disjunctive bases. Finally, we consider
the problem of giving a category-theoretic formulation of disjunctive bases,
and provide a partial solution
COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS
The ability to simulate a biological organism by employing a computer is related to the
ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b)
for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)
ODIN: Obfuscation-based privacy-preserving consensus algorithm for Decentralized Information fusion in smart device Networks
The large spread of sensors and smart devices in urban infrastructures are motivating research in the area of the Internet of Things (IoT) to develop new services and improve citizens’ quality of life. Sensors and smart devices generate large amounts of measurement data from sensing the environment, which is used to enable services such as control of power consumption or traffic density. To deal with such a large amount of information and provide accurate measurements, service providers can adopt information fusion, which given the decentralized nature of urban deployments can be performed by means of consensus algorithms. These algorithms allow distributed agents to (iteratively) compute linear functions on the exchanged data, and take decisions based on the outcome, without the need for the support of a central entity. However, the use of consensus algorithms raises several security concerns, especially when private or security critical information is involved in the computation.
In this article we propose ODIN, a novel algorithm allowing information fusion over encrypted data. ODIN is a privacy-preserving extension of the popular consensus gossip algorithm, which prevents distributed agents from having direct access to the data while they iteratively reach consensus; agents cannot access even the final consensus value but can only retrieve partial information (e.g., a binary decision). ODIN uses efficient additive obfuscation and proxy re-encryption during the update steps and garbled circuits to make final decisions on the obfuscated consensus. We discuss the security of our proposal and show its practicability and efficiency on real-world resource-constrained devices, developing a prototype implementation for Raspberry Pi devices
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