Related papers: Modular Descriptions of Regular Functions
Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.
Modern language models define distributions over strings, but downstream tasks often require different output formats. For instance, a model that generates byte-pair strings does not directly produce word-level predictions, and a DNA model…
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
In this paper we introduce the notion of Modal Software Engineering: automatically turning sequential, deterministic programs into semantically equivalent programs efficiently operating on inputs coming from multiple overlapping worlds. We…
Interaction languages such as MSC are often associated with formal semantics by means of translations into distinct behavioral formalisms such as automatas or Petri nets. In contrast to translational approaches we propose an operational…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Local grammars can be represented in a very convenient way by automata. This paper describes and illustrates an efficient algorithm for the application of local grammars put in this form to lemmatized texts.
In previous work we describe a novel approach to dependent typing based on a multivalued term language. In this technical report we formalise the runtime, a kind of operational semantics, for that language. We describe a fairly…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…