Related papers: Simple grammar bisimilarity, with an application t…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative…
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set,…
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…
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…
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…
This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…
This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and…
We investigate the following question: if a polynomial can be evaluated at rational points by a polynomial-time boolean algorithm, does it have a polynomial-size arithmetic circuit? We argue that this question is certainly difficult.…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
We present a type inference algorithm for lambda-terms in Elementary Affine Logic using linear constraints. We prove that the algorithm is correct and complete.
We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic…
We show that the equivalence of deterministic linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a…
This paper solves an open problem concerning the generative power of nonerasing context-free rewriting systems using a simple mechanism for checking for context dependencies, in the literature known as semi-conditional grammars of degree…
We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of "simple" auctions. Our framework captures all of the most prominent examples of "simple"…
As large language models (LLMs) become integral to code-related tasks, a central question emerges: Do LLMs truly understand program semantics? We introduce EquiBench, a new benchmark for evaluating LLMs through equivalence checking, i.e.,…
A test set for a formal language (set of strings) L is a subset T of L such that for any two string homomorphisms f and g defined on L, if the restrictions of f and g on T are identical functions, then f and g are identical on the entire L.…
Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally…