Related papers: On Computational Completeness of Semi-Conditional …
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Rewriting logic is a natural and expressive framework for the specification of concurrent systems and logics. The Maude specification language provides an implementation of this formalism that allows executing, verifying, and analyzing the…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
An $r$-matrix is a matrix with symbols in $\{0,1,\dots,r-1\}$. A matrix is simple if it has no repeated columns. Let the support of a matrix $F$, $\text{supp}(F)$ be the largest simple matrix such that every column in $\text{supp}(F)$ is in…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
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),…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
Constraint Grammar rules are induced from corpora. A simple scheme based on local information, i.e., on lexical biases and next-neighbour contexts, extended through the use of barriers, reached 87.3 percent precision (1.12 tags/word) at…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
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…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…