Related papers: Improvements for Free
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This…
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitrary fields. The evidence for these claims is restricting…
This paper presents rules of inference for a binary quantifier $I$ for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. $I$ binds one variable and forms a formula from two formulas.…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
No-Free-Lunch Theorems state, roughly speaking, that the performance of all search algorithms is the same when averaged over all possible objective functions. This fact was precisely formulated for the first time in a now famous paper by…
Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange…
This thesis investigates effectful declarative programming with an emphasis on non-determinism as an effect. On the one hand, we are interested in developing applications using non-determinism as underlying implementation idea. We discuss…
The No Free Lunch theorems are often used to argue that domain specific knowledge is required to design successful algorithms. We use algorithmic information theory to argue the case for a universal bias allowing an algorithm to succeed in…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
In this contribution we explore choice revision, a sort of belief change in which the new information is represented by a set of sentences and the agent could accept some of the sentences while rejecting the others. We propose a generalized…
We propose a heuristically modified FP-Tree for ontology learning from text. Unlike previous research, for concept extraction, we use a regular expression parser approach widely adopted in compiler construction, i.e., deterministic finite…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Software testing uses wide range of different tools to enhance the complicated process of defining quality of the system under test. Formal Concept Analysis (FCA) provides us with algorithms of deriving formal ontology from a set of objects…