Circular Pattern Matching with k Mismatches

Charalampopoulos, Panagiotis; Kociumaka, Tomasz; Pissis, Solon P.; Radoszewski, Jakub; Rytter, Wojciech; Straszyński, Juliusz; Waleń, Tomasz; Zuba, Wiktor

doi:10.1007/978-3-030-25027-0_15

Cited by 4 publications

(4 citation statements)

References 50 publications

(111 reference statements)

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“…Another well-known notion of lc-anchors is difference covers, which have been introduced by Burkhardt and Kärkkäinen [19] for suffix array construction in small space (see also [79]). Difference covers play also a central role in the elegant linear-time suffix array construction algorithm of Kärkkäinen et al [64]; and they have been used in other string processing applications [21,12]. Another very powerful type of lc-anchors is string synchronizing sets, which have been recently proposed by Kempa and Kociumaka [67], for constructing, among others, an optimal data structure for LCE queries (see also [31]).…”

Section: Other Related Workmentioning

confidence: 99%

“…Another very powerful type of lc-anchors is string synchronizing sets, which have been recently proposed by Kempa and Kociumaka [67], for constructing, among others, an optimal data structure for LCE queries (see also [31]). String synchronizing sets have applications in designing sublinear-time algorithms for classic string problems [22,24], whose textbook linear-time solutions rely on suffix trees. Another type of lc-anchors, very much related to string synchronizing sets, is the notion of partitioning sets [16,70].…”

Section: Other Related Workmentioning

confidence: 99%

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Text Indexing for Long Patterns: Anchors are All you Need

Ayad¹,

Loukides

Pissis

2023

Proc. VLDB Endow.

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In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to represent such string datasets in a compact form but also to simultaneously enable fast pattern matching queries. This is the classic text indexing problem. The four absolute measures anyone should pay attention to when designing or implementing a text index are: (i) index space; (ii) query time; (iii) construction space; and (iv) construction time. Unfortunately, however, most (if not all) widely-used indexes (e.g., suffix tree, suffix array, or their compressed counterparts) are not optimized for all four measures simultaneously, as it is difficult to have the best of all four worlds. Here, we take an important step in this direction by showing that text indexing with locally consistent anchors (lc-anchors) offers remarkably good performance in all four measures, when we have at hand a lower bound l on the length of the queried patterns --- which is arguably a quite reasonable assumption in practical applications. Specifically, we improve on the construction of the index proposed by Loukides and Pissis, which is based on bidirectional string anchors (bd-anchors), a new type of lc-anchors, by: (i) designing an average-case linear-time algorithm to compute bd-anchors; and (ii) developing a semi-external-memory implementation to construct the index in small space using near-optimal work. We then present an extensive experimental evaluation, based on the four measures, using real benchmark datasets. The results show that, for long patterns, the index constructed using our improved algorithms compares favorably to all classic indexes: (compressed) suffix tree; (compressed) suffix array; and the FM-index.

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Section: Other Related Workmentioning

confidence: 99%

Section: Other Related Workmentioning

confidence: 99%

Text Indexing for Long Patterns: Anchors are All you Need

Ayad¹,

Loukides

Pissis

2023

Proc. VLDB Endow.

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“…However the following lower bound [13], shows that the size of the edit distance neighborhood is too large even in the best case:…”

Section: A Brute-force Edit Distance Certificationmentioning

confidence: 99%

Certified Robustness of Learning-based Static Malware Detectors

Huang¹,

Marchant²,

Lucas³

et al. 2023

Preprint

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Certified defenses are a recent development in adversarial machine learning (ML), which aim to rigorously guarantee the robustness of ML models to adversarial perturbations. A large body of work studies certified defenses in computer vision, where ℓ 𝑝 norm-bounded evasion attacks are adopted as a tractable threat model. However, this threat model has known limitations in vision, and is not applicable to other domains-e.g., where inputs may be discrete or subject to complex constraints. Motivated by this gap, we study certified defenses for malware detection, a domain where attacks against ML-based systems are a real and current threat. We consider static malware detection systems that operate on byte-level data. Our certified defense is based on the approach of randomized smoothing which we adapt by: (1) replacing the standard Gaussian randomization scheme with a novel deletion randomization scheme that operates on bytes or chunks of an executable; and(2) deriving a certificate that measures robustness to evasion attacks in terms of generalized edit distance. To assess the size of robustness certificates that are achievable while maintaining high accuracy, we conduct experiments on malware datasets using a popular convolutional malware detection model, MalConv. We are able to accurately classify 91% of the inputs while being certifiably robust to any adversarial perturbations of edit distance 128 bytes or less. By comparison, an existing certification of up to 128 bytes of substitutions (without insertions or deletions) achieves an accuracy of 78%. In addition, given that robustness certificates are conservative, we evaluate practical robustness to several recently published evasion attacks and, in some cases, find robustness beyond certified guarantees. CCS CONCEPTS• Security and privacy → Logic and verification; Malware and its mitigation; • Computing methodologies → Machine learning.

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“…Charalampopoulos et al [8] proposed solutions for circular pattern k-mismatch problem with worst-case upper bounds. The authors proposed two efficient algorithms having O(nk)-time and O(n+ n/m k 5 )-time complexity.…”

Section: Background Workmentioning

confidence: 99%

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

2020

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AbstractPattern matching is the area of computer science which deals with security and analysis of data. This work proposes two 2D pattern matching algorithms based on two different input domains. The first algorithm is for the case when the given pattern contains only two symbols, that is, binary symbols 0 and 1. The second algorithm is in the case when the given pattern contains decimal numbers, that is, the collection of symbols between 0 and 9. The algorithms proposed in this manuscript convert the given pattern into an equivalent binary or decimal number, correspondingly find the cofactors of the same dimension and convert these cofactors into numbers if a particular cofactor number matches indicate the matching of the pattern. Furthermore, the algorithm is enhanced for decimal numbers. In the case of decimal numbers, each row of the pattern is changed to its decimal equivalent, and then, modulo with a suitable prime number changes the decimal equivalent into a number less than the prime number. If the number mismatched pattern does not exist, the complexity of the proposed algorithm is very low as compared to other traditional algorithms.

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Circular Pattern Matching with k Mismatches

Cited by 4 publications

References 50 publications

Text Indexing for Long Patterns: Anchors are All you Need

Text Indexing for Long Patterns: Anchors are All you Need

Certified Robustness of Learning-based Static Malware Detectors

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

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