Related papers: Fractal Symbolic Analysis
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
Fractal AI is a theory for general artificial intelligence. It allows deriving new mathematical tools that constitute the foundations for a new kind of stochastic calculus, by modelling information using cellular automaton-like structures…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Static program analysis is a valuable tool for any programming language that people write programs in. The prevalence of scripting languages in the world suggests programming language interpreters are relatively easy to write. Users of…
We extend a technique called Compiling Control. The technique transforms coroutining logic programs into logic programs that, when executed under the standard left-to-right selection rule (and not using any delay features) have the same…
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…
This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no…
Symbolic perturbations offer a novel approach for influencing neural representations without requiring direct modification of model parameters. The recursive regeneration of symbolic structures introduces structured variations in latent…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Large language models (LLMs) face significant token efficiency bottlenecks in code generation and logical reasoning tasks, a challenge that directly impacts inference cost and model interpretability. This paper proposes a formal framework…
The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…
Code analysis is fundamental in Software Engineering, supporting debugging, optimization, and security assessment. Human developers approach it through syntax parsing, static semantics inference, and dynamic reasoning. Traditional tools are…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
Many machine learning models have important structural tuning parameters that cannot be directly estimated from the data. The common tactic for setting these parameters is to use resampling methods, such as cross--validation or the…
This paper addresses the dichotomy between the formalization of structural and the formalization of behavioral knowledge by means of semantically lifted programs, which explore an intuitive connection between programs and knowledge graphs.…
The structures for the expression of fault-tolerance provisions into the application software are the central topic of this dissertation. Structuring techniques provide means to control complexity, the latter being a relevant factor for the…
We introduce a neuro-symbolic transformer-based model that converts flat, segmented facade structures into procedural definitions using a custom-designed split grammar. To facilitate this, we first develop a semi-complex split grammar…
Program specialization is a program transformation methodology which improves program efficiency by exploiting the information about the input data which are available at compile time. We show that current techniques for program…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…