Related papers: Denotational cost semantics for functional languag…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
Genomes may be analyzed from an information viewpoint as very long strings, containing functional elements of variable length, which have been assembled by evolution. In this work an innovative information theory based algorithm is…
Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit models to making only one attempt at a problem. Here, we explore inference compute…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…
Scaling language models to larger and deeper sizes has led to significant boosts in performance. Even though the size of these models limits their application in compute-constrained environments, the race to continually develop ever larger…
Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
We consider the language of $\Delta_0$-formulas with list terms interpreted over hereditarily finite list superstructures. We study the complexity of reasoning in extensions of the language of $\Delta_0$-formulas with non-standard list…
Predicative analysis of recursion schema is a method to characterize complexity classes like the class FPTIME of polynomial time computable functions. This analysis comes from the works of Bellantoni and Cook, and Leivant by data tiering.…
Understanding inferences and answering questions from text requires more than merely recovering surface arguments, adjuncts, or strings associated with the query terms. As humans, we interpret sentences as contextualized components of a…
Clear and concise code is necessary to ensure maintainability, so it is crucial that the software is as simple as possible to understand, to avoid bugs and, above all, vulnerabilities. There are many ways to enhance software without…
We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Large language models (LLMs) have shown impressive capabilities across a wide range of language tasks. However, their reasoning process is primarily guided by statistical patterns in training data, which limits their ability to handle novel…
Software systems that process structured inputs often lack complete and up-to-date specifications, which specify the input syntax and the semantics of input processing. While grammar mining techniques have focused on recovering syntactic…