Related papers: Improvements for Free
Reasoning models enhance problem-solving by scaling test-time compute, yet they face a critical paradox: excessive thinking tokens often degrade performance rather than improve it. We attribute this to a fundamental architectural flaw:…
The work relates to the automatic generation of logical specifications, considered as sets of temporal logic formulas, extracted directly from developed software models. The extraction process is based on the assumption that the whole…
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…
Recently, data abstraction has been studied in the context of separation logic, with noticeable practical successes: the developed logics have enabled clean proofs of tricky challenging programs, such as subject-observer patterns, and they…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical…
We develop a refinement of Whitehead's algorithm for primitive words in a free group. We generalize to subgroups, establishing a strengthened version of Whitehead's algorithm for free factors. We make use of these refinements in proving new…
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
We present a one-fits-all programmatic approach to reason about a plethora of objectives on probabilistic programs. The first ingredient is to add a reward-statement to the language. We then define a program transformation applying a…
Integrating free-text explanations to in-context learning of large language models (LLM) is shown to elicit strong reasoning capabilities along with reasonable explanations. In this paper, we consider the problem of leveraging the…
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
Automated simplification models aim to make input texts more readable. Such methods have the potential to make complex information accessible to a wider audience, e.g., providing access to recent medical literature which might otherwise be…
Current algorithms for context-free parsing inflict a trade-off between ease of understanding, ease of implementation, theoretical complexity, and practical performance. No algorithm achieves all of these properties simultaneously. Might et…
Belief revision of knowledge bases represented by a set of sentences in a given logic has been extensively studied but for specific logics, mainly propositional, and also recently Horn and description logics. Here, we propose to generalize…