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Decision trees have long been recognized as models of choice in sensitive applications where interpretability is of paramount importance. In this paper, we examine the computational ability of Boolean decision trees in deriving, minimizing,…
This paper considers the computational power of constant size, dynamic Bayesian networks. Although discrete dynamic Bayesian networks are no more powerful than hidden Markov models, dynamic Bayesian networks with continuous random variables…
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In…
Rule-based information extraction has lately received a fair amount of attention from the database community, with several languages appearing in the last few years. Although information extraction systems are intended to deal with…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…
Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…