Related papers: Combinatory Array Logic with Sums
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
We determine a reasonable upper bound for the complexity of collection from the left to multiply two elements of a finite soluble, or polycyclic, group by restricting attention to certain polycyclic presentations of the group.
Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomials with suitably generic p-adic Newton polygon. We thus…
Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
In [16], we obtained some congruences for Lucas quotients of two infinite families of Lucas sequences by studying the combinatorial sum $$\sum_{k\equiv r(\mbox{mod}m)}{n\choose k}a^k.$$ In this paper, we show that the sum can be expressed…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.
The SMT (Satisfiability Modulo Theories) theory of arrays is well-established and widely used, with variousdecision procedures and extensions developed for it. However, recent works suggest that developing tailoredreasoning for some…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the integrals of functions associated with Legendre…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…