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This article is a sketch of ideas that were once intended to appear in the author's famous series, "The Art of Computer Programming". He generalizes the notion of a context-free language from a set to a multiset of words over an alphabet.…
Shaping first year students' mind to help them master abstraction skills is as crucial as it is challenging. Although abstraction is a key competence in problem-solving (in particular in STEM disciplines), students are often found to rush…
Software architecture knowledge transfer is essential for software development, but related documentation is often incomplete or ambiguous, making oral explanations a common means. Our broader aim is to explore how such explanations might…
Soft robotics holds transformative potential for enabling adaptive and adaptable systems in dynamic environments. However, the interplay between morphological and control complexities and their collective impact on task performance remains…
Code-generating large language models translate natural language into code. However, only a small portion of the infinite space of naturalistic utterances is effective at guiding code generation. For non-expert end-user programmers,…
Transformers are widely used for solving tasks in natural language processing, computer vision, speech, and music domains. In this paper, we talk about the efficiency of transformers in terms of memory (the number of parameters),…
Formality plays a significant role in language communication, especially in low-resource languages such as Hindi, Japanese and Korean. These languages utilise formal and informal expressions to convey messages based on social contexts and…
Constraint programming is used for a variety of real-world optimisation problems, such as planning, scheduling and resource allocation problems. At the same time, one continuously gathers vast amounts of data about these problems. Current…
Transformers have made significant strides across various artificial intelligence domains, including natural language processing, computer vision, and audio processing. This success has naturally garnered considerable interest from both…
We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…
This article introduces the Clarke transform and Clarke coordinates, which present a solution to the disengagement of an arbitrary number of coupled displacement actuation of continuum and soft robots. The Clarke transform utilizes the…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
Recent work has shown that Transformers' compositional generalization is governed by \emph{complexity control}, initialization scale and weight decay, which steers training toward low-complexity reasoning solutions rather than…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…