Related papers: Boolean logic gate design principles in unconventi…
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
Nanomagnetic logic, in which the outcome of a computation is embedded into the energy hierarchy of magnetostatically coupled nanomagnets, offers an attractive pathway to implement in-memory computation. This computational paradigm avoids…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…
Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
Artificial RNA molecules with novel functionality have many applications in synthetic biology, pharmacy and white biotechnology. The de novo design of such devices using computational methods and prediction tools is a resource-efficient…
We consider an example of a quantum algorithm from the point of view of the de Broglie-Bohm formulation of quantum mechanics. For concreteness we look at two particular implementations: one using spin-1/2 particles as described by a simple…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between…
Nanoparticles interconnected by insulating organic molecules exhibit nonlinear switching behavior at low temperatures. By assembling these switches into a network and manipulating charge transport dynamics through surrounding electrodes,…
Natural language questions are inherently compositional, and many are most easily answered by reasoning about their decomposition into modular sub-problems. For example, to answer "is there an equal number of balls and boxes?" we can look…
We propose a nanostructure switch based on nuclear magnetic resonance (NMR) which offers reliable quantum gate operation, an essential ingredient for building a quantum computer. The nuclear resonance is controlled by the magic number…
Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to…
We explore the possibilities of designing classical logic gates at nano-scale level using magnetic quantum rings. A single ring is used for designing OR, NOT, XOR, XNOR and NAND gates, while AND and NOR gate responses are achieved using two…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…