String Length Research Articles

A framework for designing space-efficient dictionaries for parameterized and order-preserving matching

Let P be a collection of d patterns {P1,P2,…,Pd} of total length n characters, which are chosen from an alphabet Σ of size σ. Given a text T (over Σ), the dictionary indexing problem is to create a data structure using which we can report all positions j (called occurrences) where at least one of the patterns Pi∈P is a match with the same-length substring of T that starts at j. We consider this problem under the following definitions of matching.•Parameterized Matching: The characters of Σ are partitioned into static characters and parameterized characters. Two equal length strings S and S′ are a parameterized match iff the static characters match exactly, and there exists a one-to-one function which renames the parameterized characters in S to those in S′.•Order-Preserving Matching: The alphabet Σ is ordered. Two equal length strings S and S′ are an order-preserving match iff for any two integers i,j∈[1,|S|], S[i]≺S[j]⇔S′[i]≺S′[j], where ≺ denotes the precedence order in Σ. Let ε>0 be an arbitrarily small constant. For parameterized matching, we first present a compact O(nlog⁡σ+dlog⁡n)-bit index that reports all occ occurrences in O(|T|(log⁡σ+logσ⁡n)+occ) time, and then a succinct nlog⁡σ+o(nlog⁡σ)+O(dlog⁡n)-bit index that reports all occ occurrences in O(|T|(log⁡σ+logε⁡nlogσ⁡n)+occ) time. For order-preserving matching, we present indexes of the same sizes, but with slightly increased query time.

Maximal unbordered factors of random strings

A border of a string is a non-empty prefix of the string that is also a suffix of the string, and a string is unbordered if it has no border other than itself. Loptev, Kucherov, and Starikovskaya [CPM'15] conjectured the following: If we pick a string of length n from a fixed non-unary alphabet uniformly at random, then the expected maximum length of its unbordered factors is n−O(1). We confirm this conjecture by proving that the expected value is, in fact, n−O(σ−1), where σ is the size of the alphabet. This immediately implies that we can find such a maximal unbordered factor in linear time on average. However, we go further and show that the optimum average-case running time is in Ω(n)∩O(nlogσ⁡n) due to analogous bounds by Czumaj and Gąsieniec [CPM'00] for the problem of computing the shortest period of a uniformly random string.

Inter-theory dependency analysis for SMT string solvers

Solvers in the framework of Satisfiability Modulo Theories (SMT) have been widely successful in practice. Recently there has been an increasing interest in solvers for string constraints to address security issues in web programming, for example. To be practically useful, the solvers need to support an expressive constraint language over unbounded strings, and in particular, over string lengths. Satisfiability checking for these formulas, especially in the SMT context, is very hard; it is generally undecidable for a rich fragment. In this paper, we propose a form of dependency analysis for a rich fragment of string constraints including high-level operations such as length, contains to deal with their inter-theory interaction so as to solve them more efficiently. We implement our dependency analysis in the string theory of the Z3 solver to obtain a new one, called S3N. Finally, we demonstrate the superior performance of S3N over state-of-the-art string solvers such as Z3str3, CVC4, S3P, and Z3 on several large industrial-strength benchmarks.

Nonrelativistic spinning strings

We construct nonrelativistic spinning string solutions corresponding to SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5. Considering various nonrelativistic spinning string configurations both in AdS5 as well as S5 we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling ( sim sqrt{mathfrak{g}} ) corrections near the BPS bound have been estimated in the slow spinning limit of strings in AdS5. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along AdS5 and one along S5. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in AdS5. The rest of the paper essentially unfolds the underlying connection between SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5 and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in R × S3 as well as in certain sub-sector of AdS5 we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.

Efficient Data Structures for Range Shortest Unique Substring Queries

Let T[1,n] be a string of length n and T[i,j] be the substring of T starting at position i and ending at position j. A substring T[i,j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α,β], return a shortest substring T[i,j] of T with exactly one occurrence in [α,β]. We present an O(nlogn)-word data structure with O(logwn) query time, where w=Ω(logn) is the word size. Our construction is based on a non-trivial reduction allowing for us to apply a recently introduced optimal geometric data structure [Chan et al., ICALP 2018]. Additionally, we present an O(n)-word data structure with O(nlogϵn) query time, where ϵ>0 is an arbitrarily small constant. The latter data structure relies heavily on another geometric data structure [Nekrich and Navarro, SWAT 2012].

Online recognition of dictionary with one gap

We formalize and examine the online Dictionary Recognition with One Gap problem (DROG) which is the following. Preprocess a dictionary D of d patterns each containing a special gap symbol that matches any string, so that given a text arriving online a character at a time, all patterns from D which are suffixes of the text that has arrived so far and have not been reported yet, are reported before the next character arrives. The gap symbols are associated with bounds determining possible lengths of matching strings. Online DROG captures the difficulty in a bottleneck procedure for cyber-security, as many digital signatures of viruses manifest themselves as patterns with a single gap.Following the work on the closely related online Dictionary Matching with One Gap problem (DMOG), we provide algorithms whose time cost depends linearly on δ(GD), where GD is a bipartite graph that captures the structure of D and δ(GD) is the degeneracy of this graph. These algorithms are of practical interest since although δ(GD) can be as large as d, and even larger if GD is a multi-graph, it is typically a small constant in practice.

CYK Parsing over Distributed Representations

Parsing is a key task in computer science, with applications in compilers, natural language processing, syntactic pattern matching, and formal language theory. With the recent development of deep learning techniques, several artificial intelligence applications, especially in natural language processing, have combined traditional parsing methods with neural networks to drive the search in the parsing space, resulting in hybrid architectures using both symbolic and distributed representations. In this article, we show that existing symbolic parsing algorithms for context-free languages can cross the border and be entirely formulated over distributed representations. To this end, we introduce a version of the traditional Cocke–Younger–Kasami (CYK) algorithm, called distributed (D)-CYK, which is entirely defined over distributed representations. D-CYK uses matrix multiplication on real number matrices of a size independent of the length of the input string. These operations are compatible with recurrent neural networks. Preliminary experiments show that D-CYK approximates the original CYK algorithm. By showing that CYK can be entirely performed on distributed representations, we open the way to the definition of recurrent layer neural networks that can process general context-free languages.

An Ultralow Complexity String Matching Approach to Screen Content Coding in AVS3

Screen content coding (SCC) is increasingly used in mobile devices, and ultralow coding complexity is required for low power consumption. This article proposes an ultralow complexity string matching approach to SCC. The proposed approach has two essential features: 1) allowing only two types of most effective reference strings that have two most frequently occurring values of offset (i.e., displacement vector) named dual unity offset and 2) fully optimized coding of string matching parameters for maximum coding efficiency. Since at most only two offset values and corresponding reference string positions are allowed for any current string being coded, the optimal reference string searching process is extremely simple and only needs to select the best string from at most two candidates. Moreover, in the proposed approach, the value ranges of string matching parameters, i.e., the string offset vector and string length are very limited, resulting in few bits to code the two parameters and high coding efficiency. Compared with the AVS3 reference software HPM7.0 with IBC disabled, using AVS3 SCC common test condition and YUV test sequences in text and graphics with motion category, the proposed technique achieves Y average BD-rate reduction of 10.8% and 5.8% for all intra (AI) and low-delay B (LDB) configurations, respectively, at ultralow encoding and decoding complexity.

Resolving Interoperability Issues of Precision and Array with Null Value of Web Services Using WSIG-JADE Framework

Web services and agent technology play a significant role while resolving the issues related to platform interoperability. Web service interoperability organization (WS-I) provided the guidelines to remove the interoperability issues using basic profile 1.1/1.2 product. However, issues are still arising while transferring the precision values and an array with null values between different platforms like JAVA and .NET. As in a precision issue, JAVA supports data precision up to the 6th value and .NET up to the 5th value after the decimal and after increasing their limits, the whole number gets rounded off. In array with a null value issue, JAVA treats null as a value but .NET treats null as an empty string. To remove these issues, we use the WSIG-JADE framework that helps to build and demonstrate a multiagent system that does the mapping and conversions between agents and web services. It limits the number of digits to the 5th place after the decimal thereby increasing the precision in data sets, whereas it treats null as an empty string so that string length remains the same for both the platforms thereby helping in the correct count of data elements.

High Entropy Random Selection Protocols

We study the two party problem of randomly selecting a common string among all the strings of length n. We want the protocol to have the property that the output distribution has high Shannon entropy or high min entropy, even when one of the two parties is dishonest and deviates from the protocol. We develop protocols that achieve high, close to n, Shannon entropy and simultaneously min entropy close to n/2. In the literature the randomness guarantee is usually expressed in terms of “resilience”. The notion of Shannon entropy is not directly comparable to that of resilience, but we establish a connection between the two that allows us to compare our protocols with the existing ones. We construct an explicit protocol that yields Shannon entropy $$n - O(1)$$ and has $$O(\log ^* n)$$ rounds, improving over the protocol of Goldreich et al. (SIAM J Comput 27: 506–544, 1998) that also achieves this entropy but needs O(n) rounds. Both these protocols need $$O(n^2)$$ bits of communication. Next we reduce the number of rounds and the length of communication in our protocols. We show the existence, non-explicitly, of a protocol that has 6 rounds, O(n) bits of communication and yields Shannon entropy $$n- O(\log n)$$ and min entropy $$n/2 - O(\log n)$$ . Our protocol achieves the same Shannon entropy bound as, also non-explicit, protocol of Gradwohl et al. (in: Dwork (ed) Advances in Cryptology—CRYPTO ‘06, 409–426, Technical Report , 2006), however achieves much higher min entropy: $$n/2 - O(\log n)$$ versus $$O(\log n)$$ . Finally we exhibit a very simple 3-round explicit “geometric” protocol with communication length O(n). We connect the security parameter of this protocol with the well studied Kakeya problem motivated by Harmonic Analysis and Analytic Number Theory. We prove that this protocol has Shannon entropy $$n-o(n)$$ . Its relation to the Kakeya problem follows a new and different approach to the random selection problem than any of the previously known protocols.

Pseudorapidity Dependence of Multiplicity Fluctuations in a Model of Interacting Quark–Gluon Strings of Finite Rapidity Length

The paper shows results obtained for event-by-event multiplicity fluctuations studied in terms of strongly intensive quantity in the Monte Carlo model of quark–gluon strings of finite pseudorapidity length. The effect of the string fusion on the fluctuation measure is presented as its dependence on the distance between the intervals of pseudorapidity in which multiplicity is determined. The results are in qualitative agreement with experimental data on Pb+Pb collisions by the ALICE experiment at the LHC.

ТАМПОНАЖНІ РОЗЧИНИ З ДИФЕРЕНЦІЙОВАНИМ ТЕМПОМ НАБОРУ МІЦНОСТІ

Based on the analyzing of industrial materials has been established that lot of gas wells characterized of inter-string flows and could not been effective be on stream. The article has been shown, that main base of this problem is poor quality well cementing, first off all the interval of reservoir horizon. After researched of information of well cementing has been ascertained that first eight hour of the curing of cement is attended by drop of the hydrostatic pressure. It becomes the main reason of oil and gas inflow. The drop of cement stone sealing properties during long time maintenance is result of poor cement stone resistance to thermocorrosion in the subsurface conditions. This is the reason that new cementing slurry recipe should be prepared. This recipes should be provides a differentiated rate of strength gain during the time of waiting the cement in conditions with high technological properties for long time maintenance. One of the most dangerous process during well construction is oil and gas inflow or inter-string flows in time of wait-on-cement time. This time is characterized special conditions of cement stone, because it represents as permeable matrix with hydration products, and with porous full by water. It is the best conditions for the flow of fluid throw pores. It can be the reason of suffusion channeling. In order to prevent for oil and gas inflow the article has been invited the achieve optimal distribution the pressure. For the realized this purpose can been used cementing process with two cement slurry batch with different setting up time. In practice of cementing of casing with length of section capital string, which shut off the gas more than 400 m, use differentiation the wait-on-cement time the portion of cementing slurry with length of cement column. In result start of time wait-on-cement in the bottom portion should be less for 2-3 hour than top portion. Keywords: water-mixture ratio, rheological properties, wellbore pressure, component of cement mortar column, cement mortars, cement mortar hardening, rate of strength gain, strength of cement ring

Structure of the space of taboo-free sequences

Models of sequence evolution typically assume that all sequences are possible. However, restriction enzymes that cut DNA at specific recognition sites provide an example where carrying a recognition site can be lethal. Motivated by this observation, we studied the set of strings over a finite alphabet with taboos, that is, with prohibited substrings. The taboo-set is referred to as mathbb {T} and any allowed string as a taboo-free string. We consider the so-called Hamming graph varGamma _n(mathbb {T}), whose vertices are taboo-free strings of length n and whose edges connect two taboo-free strings if their Hamming distance equals one. Any (random) walk on this graph describes the evolution of a DNA sequence that avoids taboos. We describe the construction of the vertex set of varGamma _n(mathbb {T}). Then we state conditions under which varGamma _n(mathbb {T}) and its suffix subgraphs are connected. Moreover, we provide an algorithm that determines if all these graphs are connected for an arbitrary mathbb {T}. As an application of the algorithm, we show that about 87% of bacteria listed in REBASE have a taboo-set that induces connected taboo-free Hamming graphs, because they have less than four type II restriction enzymes. On the other hand, four properly chosen taboos are enough to disconnect one suffix subgraph, and consequently connectivity of taboo-free Hamming graphs could change depending on the composition of restriction sites.

Online parameterized dictionary matching with one gap

We study the online Parameterized Dictionary Matching with One Gap problem (PDMOG) which is the following. Preprocess a dictionary D of d patterns, where each pattern contains a special gap symbol that can match any string, so that given a text T arriving online, a character at a time, we can report all the patterns from D that parameterized match to suffixes of the text that has arrived so far, before the next character arrives. Two equal-length strings are a parameterized match if there exists a bijection on the alphabets, such that one string matches the other under the bijection. The gap symbols are associated with bounds determining the possible lengths of matching strings. Online Dictionary Matching with One Gap (DMOG) captures the difficulty in a bottleneck procedure for cyber-security, as many digital signatures of viruses manifest themselves as patterns with a single gap. Parameterized match captures possible encryption of the patterns. We also define the strict PDMOG problem, in which subpatterns of the same dictionary pattern should be parameterized matched via the same bijection. This captures situations where subpatterns of a dictionary pattern are encoded simultaneously. We study this problem for special case called alphabet-saturated dictionairy, where every subpattern contains all characters of the dictionary alphabet Σ. We use the following parameters to describe our results: D is the total size of the dictionary (not including the gaps), plsc is the longest parameterized suffix chain of subpatterns in D, op is the number of parameterized patterns occurrences in T, α⁎ and β⁎ are the minimum left and maximum right gap borders in the non-uniformly bounded dictionary case, δ(GD) is the degeneracy of the graph GD representing dictionary D. This graph is classified as sparse or dense according the value of the δ(GD) and plsc parameters. We obtain:–O˜(D) preprocessing time/space and O˜(δ(GD)⋅plsc+plsc⋅max⁡{|Σ|,M}+op) query time per text character algorithm for online PDMOG with sparse graph dictionaries.–O˜(D+d(β⁎−α⁎)) preprocessing time/space and O˜(plsc⋅d⋅(β⁎−α⁎)+plsc⋅max⁡{|Σ|,M}+op) query time per text character algorithm for online PDMOG with dense graph dictionaries.–O˜(D) preprocessing time/space and O˜(δ(GD)⋅plsc+op) query time per text character algorithm for strict PDMOG with alphabet-saturated dictionaries.These results are parallel to the ones obtained for the Dictionary with One Gap (DMOG) problem almost matching the lower bounds achieved for this problem [7]. While the parameter δ(GD) can be as large as d and much lager if the dictionary has non-uniform gap boundaries, and the parameter plsc could theoretically be as large as d, in many practical situations these parameters are actually small. The strength of our work is in achieving results that explore and exploit small values for these parameters, thus supplying algorithms that are suitable for some practical cyber security needs.

Finding patterns and periods in Cartesian tree matching

We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching, multiple pattern matching, and indexing problems. We propose a linear time algorithm for single pattern matching, and randomized linear time algorithms for multiple pattern matching and indexing. We also define three types of periods, called full period, initial period, and general period. We propose O(n) time, O(nlog⁡log⁡n) time, and O(nlog⁡n) time algorithms for finding all the full periods, initial periods, and general periods of a string of length n, respectively. Our efficient algorithms use a representation of the Cartesian tree, called parent-distance representation.

Solving longest common subsequence problems via a transformation to the maximum clique problem

Longest common subsequence problems find various applications in bioinformatics, data compression and text editing, just to name a few. Even though numerous heuristic approaches were published in the related literature for many of the considered problem variants during the last decades, solving these problems to optimality remains an important challenge. This is particularly the case when the number and the length of the input strings grows. In this work we define a new way to transform instances of the classical longest common subsequence problem and of some of its variants into instances of the maximum clique problem. Moreover, we propose a technique to reduce the size of the resulting graphs. Finally, a comprehensive experimental evaluation using recent exact and heuristic maximum clique solvers is presented. Numerous, so-far unsolved problem instances from benchmark sets taken from the literature were solved to optimality in this way.

Dashed strings for string constraint solving

String processing is ubiquitous across computer science, and arguably more so in web programming — where it is also a critical part of security issues such as injection attacks. In recent years, a number of string solvers have been developed to solve combinatorial problems involving string variables and constraints. We examine the dashed string approach to string constraint solving, which represents an unknown string as a sequence of blocks of characters with bounds on their cardinalities. The solving approach relies on propagation of information about the blocks of characters that arise from reasoning about the constraints in which they occur. This approach shows promising performance on many benchmarks involving constraints like string length, equality, concatenation, and regular expression membership. In this paper, we formally review the definition, the properties and the use of dashed strings for string constraint solving, and we provide an empirical validation that confirms the effectiveness of this approach.

Efficient Logspace Classes for Enumeration, Counting, and Uniform Generation

We study two simple yet general complexity classes, which provide a unifying framework for efficient query evaluation in areas like graph databases and information extraction, among others. We investigate the complexity of three fundamental algorithmic problems for these classes: enumeration, counting and uniform generation of solutions, and show that they have several desirable properties in this respect. Both complexity classes are defined in terms of non deterministic logarithmic-space transducers (NL transducers). For the first class, we consider the case of unambiguous NL transducers, and we prove constant delay enumeration, and both counting and uniform generation of solutions in polynomial time. For the second class, we consider unrestricted NL transducers, and we obtain polynomial delay enumeration, approximate counting in polynomial time, and polynomialtime randomized algorithms for uniform generation. More specifically, we show that each problem in this second class admits a fully polynomial-time randomized approximation scheme (FPRAS) and a polynomial-time Las Vegas algorithm (with preprocessing) for uniform generation. Remarkably, the key idea to prove these results is to show that the fundamental problem #NFA admits an FPRAS, where #NFA is the problem of counting the number of strings of length n (given in unary) accepted by a non-deterministic finite automaton (NFA). While this problem is known to be #P-complete and, more precisely, SpanL-complete, it was open whether this problem admits an FPRAS. In this work, we solve this open problem, and obtain as a welcome corollary that every function in SpanL admits an FPRAS.

Fuzzy C-Means Cluster Analysis Based on Variable Length String Genetic Algorithm for the Grouping of Rock Discontinuity Sets

Discontinuities have huge impact on civil and mining engineering. To understand the spatial features of discontinuities, it is common to group them into different sets based on orientation. In this paper, a new algorithm is introduced for the identification of discontinuity sets. The new algorithm is developed by combined fuzzy C-means algorithm with variable length string genetic algorithm. In the new method, the number of discontinuity sets is not the necessary input parameter any more. This method is robust, global optimal and totally automatic. To verify its validity, the new method was firstly applied to an artificial data as well as a published data. For artificial data set, the assignment error rate is only 7.4%. For published data set, only 2 discontinuities are assigned to wrong sets. The results indicate that the new algorithm is better than fuzzy C-means algorithm and comparable with other common methods. Afterwards, the new method was utilized to analyze the orientation data sampled at an underground storage cavern site. The new method determines that the ideal number of sets is 3. The new method provided satisfactory results, which confirm its effectiveness and convenience.

Robust security framework with bit‐flipping attack and timing attack for key derivation functions

A Key Derivation Function (KDF) derives cryptographic keys from private string and public information. The security property for the cryptographic keys is indistinguishable from the random strings of equal length. The security analysis of KDFs has received increasing attention. The practice important of KDFs is reflected in the adoption of industry standards such as NIST800-135 and PKCS5. This study proposes a robust security framework that takes into consideration the side-channel attacks. The robust security framework consists of the proposed security model and existing security models. The proposed security model is known as Adaptive Chosen All Inputs Model (CAM), which analyses the security of KDFs in terms of the bit-flipping attack and timing attack. The existing security model is the Adaptive Chosen Public Inputs Model (CPM). This research shows the implication of relationship and the non-implication relationship between CAM and CPM. The simulation of security models is according to the indistinguishable game played between a challenger and an adversary. These security models are used to evaluate existing KDFs. The result shows that none of the existing KDFs are secure in CAM for both the bit-flipping attack and timing attack. Hence, this research introduces an alternative KDF that is proven secure in CAM.