Related papers: Computing with Hereditarily Finite Sequences
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
It is argued that transformation processes (generation rules) showing evidence of a long evolutionary history in universal computing systems can be generalized. The explicit function class $ \Omega $ is defined as follows: "Operators whose…
In 2014, Ungar et al. proposed Korz, a new computational model for structuring adaptive (object-oriented) systems. Korz combines implicit parameters and multiple dispatch to structure the behavior of objects in a multidimensional space.…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control, PD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PD0L words. We…
First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…
In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical…
Language models frequently produce plausible yet incorrect reasoning traces that are difficult to verify. We investigate fine-tuning models to use Prolog as an external symbolic reasoning tool, training Qwen2.5-3B-Instruct with Group…
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We present a new approach for building source-to-source transformations that can run on multiple programming languages, based on a new way of representing programs called incremental parametric syntax. We implement this approach in Haskell…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…