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Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of…
Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
Context. Variability-intensive programs (program families) appear in many application areas and for many reasons today. Different family members, called variants, are derived by switching statically configurable options (features) on and…
Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
The goal of grammar compression is to construct a small sized context free grammar which uniquely generates the input text data. Among grammar compression methods, RePair is known for its good practical compression performance. MR-RePair…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality…