相关论文: Compaction of Church Numerals for Higher-Order Com…
We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on $n$ nodes labeled from an alphabet of size $\sigma$, for which the size of the top DAG is…
Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term…
Pattern-matching-based document-compression systems (e.g. for faxing) rely on finding a small set of patterns that can be used to represent all of the ink in the document. Finding an optimal set of patterns is NP-hard; previous compression…
Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of binary lambda terms with $m$ free indices and of size $n$…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
We introduce a variant of linear logic with second order quantifiers and type fixpoints, both restricted to purely linear formulas. The Church encodings of binary words are typed by a standard non-linear type `Church,' while the Scott…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…
For each natural number $n$, let $C^{(n)}$ be the closed and unbounded proper class of ordinals $\alpha$ such that $V_\alpha$ is a $\Sigma_n$ elementary substructure of $V$. We say that $\kappa$ is a \emph{$C^{(n)}$-cardinal} if it is the…
A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It…
The main goal of 1-bit compressive sampling is to decode $n$ dimensional signals with sparsity level $s$ from $m$ binary measurements. This is a challenging task due to the presence of nonlinearity, noises and sign flips. In this paper, the…
This paper proposes a novel method that can replace compression-based dissimilarity measure (CDM) in composer estimation task. The main features of the proposed method are clarity and scalability. First, since the proposed method is…
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and…
We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…
Term Coding asks: given a finite system of term identities $\Gamma$ in $v$ variables, how large can its solution set be on an $n$--element alphabet, when we are free to choose the interpretations of the function symbols? This turns familiar…
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on…
The biggest cost of computing with large matrices in any modern computer is related to memory latency and bandwidth. The average latency of modern RAM reads is 150 times greater than a clock step of the processor. Throughput is a little…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…