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In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming.…
The amount of completely sequenced chloroplast genomes increases rapidly every day, leading to the possibility to build large scale phylogenetic trees of plant species. Considering a subset of close plant species defined according to their…
Phonology, as it is practiced, is deeply computational. Phonological analysis is data-intensive and the resulting models are nothing other than specialized data structures and algorithms. In the past, phonological computation - managing…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…
The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. The focusing…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
Computational tools for data analysis are being released daily on repositories such as the Comprehensive R Archive Network. How we integrate these tools to solve a problem in research is increasingly complex and requiring frequent updates.…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Computational morphology handles the language processing at the word level. It is one of the foundational tasks in the NLP pipeline for the development of higher level NLP applications. It mainly deals with the processing of words and word…
To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…