Related papers: Dynamic Tangled Derivative Logic of Metric Spaces
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…
Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They…
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
A scheme for logical computation using non-linear dynamical systems is presented. Examples of discrete-time maps configured as AND, OR, NAND and NOR gates are given. It is seen that the logical operations are flexible in the sense that an…
The computability power of a distributed computing model is determined by the communication media available to the processes, the timing assumptions about processes and communication, and the nature of failures that processes can suffer. In…
The aim of this paper is threefold. Firstly, we develop the author's previous work on the dynamical relationship between determinantal point processes and CAR algebras. Secondly, we present a novel application of the theory of stochastic…