Related papers: Program algebra for random access machine programs

Threads as considered in thread algebra model behaviours to be controlled by some execution environment: upon each action performed by a thread, a reply from its execution environment -- which takes the action as an instruction to be…

One of the most well established brain principles, hebbian learning, has led to the theoretical concept of neural assemblies. Based on it, many interesting brain theories have spawned. Palm's work implements this concept through binary…

Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…

Reinforcement Learning (RL) is a learning paradigm in which the agent learns from its environment through trial and error. Deep reinforcement learning (DRL) algorithms represent the agent's policies using neural networks, making their…

Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…

While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…

This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

We propose a novel, operational framework to formally describe the semantics of concurrent programs running within the context of a relaxed memory model. Our framework features a "temporary store" where the memory operations issued by the…

The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…

We perceive programs as single-pass instruction sequences. A single-pass instruction sequence under execution is considered to produce a behaviour to be controlled by some execution environment. Threads as considered in basic thread algebra…

A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of…

This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…

This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Neural networks are regarded as systems whose connections are Lagrangian variables, namely functions depending on…

We propose novel iterative learning control algorithms to track a reference trajectory in resource-constrained control systems. In many applications, there are constraints on the number of control actions, delivered to the actuator from the…

We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms.…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

Empirically, neural networks that attempt to learn programs from data have exhibited poor generalizability. Moreover, it has traditionally been difficult to reason about the behavior of these models beyond a certain level of input…