Related papers: Number representations and term rewriting

Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…

Integer iteration rules such as n |-> {a n + b, c n +d} are studied as minimal examples of the general process of multicomputation. Despite the simplicity of such rules, their multiway graphs can be complex, exhibiting, for example,…

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…

In the research on computational effects, defined algebraically, effect symbols are often expected to obey certain equations. If we orient these equations, we get a rewrite system, which may be an effective way of transforming or optimizing…

For the whole class of linear term rewriting systems, we define \emph{bottom-up rewriting} which is a restriction of the usual notion of rewriting. We show that bottom-up rewriting effectively inverse-preserves recognizability and analyze…

We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional…

We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…

We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated posets on vertices generalize Barnard--McConville's flip order for graph-associahedra,…

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…

We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting…

We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the…

We introduce a generic presentation of 'syntactic objects built by mixed induction and coinduction' encompassing all standard kinds of infinitary terms, as well as derivation trees in non-wellfounded proof systems. We then define a notion…

Despite deep recurrent neural networks (RNNs) demonstrate strong performance in text classification, training RNN models are often expensive and requires an extensive collection of annotated data which may not be available. To overcome the…

The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…

While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…

We introduce Associative Commutative Distributive Term Rewriting (ACDTR), a rewriting language for rewriting logical formulae. ACDTR extends AC term rewriting by adding distribution of conjunction over other operators. Conjunction is vital…

We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…