Arbitrary String Research Articles

Chemical and linguistic considerations for encoding Chinese characters: an embodiment using chain-end degradable sequence-defined oligourethanes created by consecutive solid phase click chemistry.

Sequence-defined polymers (SDPs) are currently being investigated for use as information storage media. As the number of monomers in the SDPs increases, with a corresponding increase in mathematical base, the use of tandem-MS for de novo sequencing becomes more challenging. In contrast, chain-end degradation routines are truly de novo, potentially allowing very large mathematical bases for encoding. While alphabetic scripts have a few dozen symbols, logographic scripts, such as Chinese, can have several thousand symbols. Using a new in situ consecutive click reaction approach on an oligourethane backbone for writing, and a previously reported chain-end degradation routine for reading, we encoded/decoded a confucius proverb written in Chinese characters using two encoding schemes: Unicode and Zhèng Mă. Unicode is an internationally standardized arbitrary string of hexadecimal (base-16) symbols which efficiently encodes uniquely identifiable symbols but requires complete fidelity of transmission, or context-based inferential strategies to be interpreted. The Zhèng Mă approach encodes with a base-26 system using the visual characteristics and internal composition of Chinese characters themselves, which leads to greater ambiguity of encoded strings, but more robust retrievability of information from partial or corrupted encodings. The application of information-encoded oligourethanes to two different encoding systems allowed us to establish their flexibility and versatility for data storage. We found the oligourethanes immensely adaptable to both encoding schemes for Chinese characters, and we highlight the expected tradeoff between the efficiency and uniqueness of Unicode encoding on the one hand, and the fidelity to a scripts' particular visual characteristics on the other.

Exact large charge in mathcal{N} = 4 SYM and semiclassical string theory

In four-dimensional mathcal{N} = 4 super Yang-Mills theory with gauge group SU(N), we present a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge. These integrated correlators are shown to be equivalent to a one-dimensional semi-infinite lattice of harmonic oscillators with nearest-neighbor interactions, evolving over the fundamental domain of SL(2, ℤ). The solution, exceptionally simple in an SL(2, ℤ)-invariant eigenbasis, is exact in the R-charge p, rank N, and complexified gauge coupling τ. This permits a systematic and non-perturbative large charge expansion for any N and τ. Especially novel is a double-scaled “gravity regime” in which p ~ N2 ≫ 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS5 × S5. Our results in this limit provide a holographic computation of integrated semiclassical string amplitudes at arbitrary string coupling, including an emergent string scale with a large charge dressing factor. We compare to extremal correlators in superconformal QCD, for which we predict new genus expansions at large charge scaling with N.

Coding for Polymer-Based Data Storage

Polymer-based data-storage platforms use chains of binary synthetic polymers as recording media and read the content via tandem mass spectrometers. For such systems, we propose the first known family of codes that allows for both unique string reconstruction and correction of multiple mass errors. We consider two approaches: The first approach pertains to asymmetric error-correction and it is based on introducing redundancy that scales linearly with the number of errors and logarithmically with the length of the string. The construction allows for the string to be uniquely reconstructed based only on its erroneous substring composition multiset. The key idea behind our unique reconstruction approach is to interleave (shifted) Catalan-Bertrand strings with arbitrary binary strings and “reflect” them so as to force prefixes and suffixes of the same length to have different weights. The asymptotic code rate of the scheme is one, and decoding is accomplished via a simplified version of the Backtracking algorithm used for the Turnpike problem. For symmetric errors, we use a polynomial characterization of the mass information and adapt polynomial evaluation code constructions for this setting. In the process, we develop new efficient decoding algorithms for a constant number of composition errors.

A code-based hybrid signcryption scheme

Abstract A key encapsulation mechanism ( KEM {\mathsf{KEM}} ) that takes as input an arbitrary string, i.e., a tag, is known as tag- KEM {\mathsf{KEM}} , while a scheme that combines signature and encryption is called signcryption. In this article, we present a code-based signcryption tag- KEM {\mathsf{KEM}} scheme. We utilize a code-based signature and an IND - CCA2 {\mathsf{IND}}\hspace{0.1em}\text{-}\hspace{0.1em}{\mathsf{CCA2}} (adaptive chosen ciphertext attack) secure version of McEliece’s encryption scheme. The proposed scheme uses an equivalent subcode as a public code for the receiver, making the NP-completeness of the subcode equivalence problem be one of our main security assumptions. We then base the signcryption tag- KEM {\mathsf{KEM}} to design a code-based hybrid signcryption scheme. A hybrid scheme deploys asymmetric- as well as symmetric-key encryption. We give security analyses of both our schemes in the standard model and prove that they are secure against IND - CCA2 {\mathsf{IND}}\hspace{0.1em}\text{-}\hspace{0.1em}{\mathsf{CCA2}} (indistinguishability under adaptive chosen ciphertext attack) and SUF - CMA {\mathsf{SUF}}\hspace{0.1em}\text{-}\hspace{0.1em}{\mathsf{CMA}} (strong existential unforgeability under chosen message attack).

Polynomial-time trace reconstruction in the smoothed complexity model

In the trace reconstruction problem , an unknown source string x ∈ {0, 1} n is sent through a probabilistic deletion channel which independently deletes each bit with probability δ and concatenates the surviving bits, yielding a trace of x . The problem is to reconstruct x given independent traces. This problem has received much attention in recent years both in the worst-case setting where x may be an arbitrary string in {0, 1} n [DOS19, NP17, HHP18, HL20, Cha21a, Cha21b] and in the average-case setting where x is drawn uniformly at random from {0, 1} n [PZ17, HPP18, HL20, Cha21a, Cha21b]. This paper studies trace reconstruction in the smoothed analysis setting, in which a “worst-case” string x worst is chosen arbitrarily from {0, 1} n , and then a perturbed version x of x worst is formed by independently replacing each coordinate by a uniform random bit with probability σ . The problem is to reconstruct x given independent traces from it. Our main result is an algorithm which, for any constant perturbation rate 0 < σ < 1 and any constant deletion rate 0 < δ < 1, uses poly( n ) running time and traces and succeeds with high probability in reconstructing the string x. This stands in contrast with the worst-case version of the problem, for which \(\text{exp}(\tilde{O}(n^{1/5})) \) is the best known time and sample complexity [Cha21b]. Our approach is based on reconstructing x from the multiset of its short subwords and is quite different from previous algorithms for either the worst-case or average-case versions of the problem. The heart of our work is a new poly( n )-time procedure for reconstructing the multiset of all O (log n )-length subwords of any source string x ∈ {0, 1} n given access to traces of x .

Efficient Key Exchange Using Identity-Based Encryption in Multipath TCP Environment

Across the globe, wireless devices with Internet facilities such as smartphones and tablets have become essential assets for communication and entertainment alike for everyday life for millions of people, which increases the network traffic and the demand for low-latency communication networks. The fourth-generation (4G)/long-term evolution (LTE)/ fifth-generation (5G) communication technology offers higher bandwidth and low latency services, but resource utilization and resiliency cannot be achieved, as transmission control protocol (TCP) is the most common choice for most of the state-of-art applications for the transport layer. An extension of TCP—multipath TCP (MPTCP)—offers higher bandwidth, resiliency, and stable connectivity by offering bandwidth aggregation and smooth handover among multiple paths. However, MPTCP uses multiple disjointed paths for communication to offer multiple benefits. A breach in the security of one of the paths may have a negative effect on the overall performance, fault-tolerance, robustness, and quality of service (QoS). In this paper, the research focuses on how MPTCP options such as MP_CAPABLE, ADD_ADDR, etc., can be used to exploit the vulnerabilities to launch various attacks such as session hijacking, traffic diversion, etc., to compromise the availability, confidentiality, and integrity of the data and network. The probable security solutions for securing MPTCP connections are analyzed, and the secure key exchange model for MPTCP (SKEXMTCP) based on identity-based encryption (IBE) is proposed and implemented. The parameters exchanged during the initial handshake are encrypted using IBE to prevent off-path attacks by removing the requirement for key exchange before communication establishment by allowing the use of arbitrary strings as a public key for encryption. The experiments were performed with IBE and an elliptic curve cryptosystem (ECC), which show that IBE performs better, as it does not need to generate keys while applying encryption. The experimental evaluation of SKEXMTCP in terms of security and performance is carried out and compared with existing solutions.

The exact [formula omitted] symmetry of string theory

By using on-shell recursion relation of string scattering amplitudes (SSA), we show that all n-point SSA of the open bosonic string theory can be expressed in terms of the Lauricella functions. This result extends the previous exact SL(K+3,C) symmetry of the 4-point Lauricella SSA (LSSA) of three tachyons and one arbitrary string states to the whole tree-level open bosonic string theory. Moreover, we present three applications of the SL(K+3,C) symmetry on the SSA. They are the solvability of all n-point SSA in terms of four-tachyon amplitudes, the existence of iteration relations among residues of a given SSA so as to soften its hard scattering behavior and finally the re-derivation of infinite linear relations among hard SSA [12].

Continuous-time quantum hash function based on one-dimensional cycle lattice

The proposed quantum hash function (QHF) based on the discrete-time quantum walk (DTQW) structure requires enlarging the coin state space and the preparation of continuous quantum states is less difficult. Hence, a new construction method of QHF is proposed based on the continuous-time quantum walk (CTQW) of the one-dimensional (1D) lattice with boundary constraints and without additional coin space. In the scheme, the input of the QHF is an arbitrary binary string message which is used to control the selected Hamiltonian of CTQW at each time interval, and the output of the QHF is the final probability distribution of CTQW. Under the same computing environment, simulation and analysis indicate that our QHF can satisfy the same security requirements such as sensitivity, diffusion and confusion, collision, birthday attack, but the collision rate is reduced by 40% without reducing effectiveness.

Growth Functions, Rates and Classes of String-Based Multiway Systems

Inspired by the recently emerging Wolfram Physics Project where “Multiway Systems,” graph representations of abstract rewriting systems equipped with a causal structure, have played an important role in discrete models of spacetime and quantum mechanics, this paper establishes several more fundamental properties about the growth (number of states over steps in a system’s evolution) of string rewriting systems in general. While proving the undecidability of exactly determining a system’s growth function, we show several asymptotic properties all growth functions of arbitrary string rewriting systems share. Through an explicit construction, it is proven that string rewriting systems, while never exceeding exponential functions in their growth, are capable of growing arbitrarily slowly, that is, slower than the asymptotic inverse of every Turing-computable function. Additionally, an elementary classification scheme partitioning the set of string rewriting systems into finitely many nontrivial subsets is provided. By introducing arithmetic-like operations under which Multiway Systems form a weakened semiring structure, it is furthermore demonstrated that their growth functions, while always being primitively recursive, can approximate many well-known elementary functions classically used in calculus, which underlines the complexity and computational diversity of Multiway Systems. In the context of the Wolfram Physics Project, some implications of these findings are discussed as well.

Sequence graph transform (SGT): a feature embedding function for sequence data mining

Sequence feature embedding is a challenging task due to the unstructuredness of sequences—arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding function, that can extract a varying amount of short- to long-term dependencies without increasing the computation is proposed. SGT’s properties are analytically proved for interpretation under normal and uniform distribution assumptions. SGT features yield significantly superior results in sequence clustering and classification with higher accuracy and lower computation as compared to the existing methods, including the state-of-the-art sequence/string Kernels and LSTM.

Owner-Enabled Secure Authorized Keyword Search Over Encrypted Data With Flexible Metadata

Metadata plays an essential role in facilitating data organizing, finding, and understanding, but it also contains lots of sensitive information about the data and the data users, e.g., the location where a picture was taken. In practice, when sensitive data is encrypted before being uploaded to untrusted public clouds, an oblivious dilemma comes: if the metadata is totally encrypted, and its functionalities no longer exist; otherwise, sensitive information may be leaked. Hence, a secure and flexible mechanism for processing different fields (marked private or public for different scenario needs) of metadata simultaneously is desirable. We searched the literature for methods of achieving such a goal, it turned out that this was not explicitly considered or reasonably solved before. Therefore, in this paper, we investigate the problem of constructing privacy-enhancing metadata, namely, 1) flexible and tamper-resistant metadata setting, 2) owner-enabled secure search authorization with explicit metadata. Based on the concept of public key encryption with keyword search (PEKS), we propose a novel Authorized Keyword Search over Encrypted Data with Metadata scheme (MD-AKS), which firstly well addressed the above demands. We formalize the security model and prove the security of MD-AKS scheme. Our work maximizes the flexibility of metadata setting in two aspects: the associated metadata can be set as an arbitrary string and the costs of clients are independent of explicit metadata’s complexity. We implement MD-AKS, the theoretical comparison and experiment results further demonstrate the usability and scalability.

Functional Encryption for Pattern Matching with a Hidden String

We propose a new functional encryption for pattern matching scheme with a hidden string. In functional encryption for pattern matching (FEPM), access to a message is controlled by its description and a private key that is used to evaluate the description for decryption. In particular, the description with which the ciphertext is associated is an arbitrary string w and the ciphertext can only be decrypted if its description matches the predicate of a private key which is also a string. Therefore, it provides fine-grained access control through pattern matching alone. Unlike related schemes in the literature, our scheme hides the description that the ciphertext is associated with. In many practical scenarios, the description of the ciphertext cannot be public information as an attacker may abuse the message description to identify the data owner or classify the target ciphertext before decrypting it. Moreover, some data owners may not agree to reveal any ciphertext information since it simply gives greater advantage to the adversary. In this paper, we introduce the first FEPM scheme with a hidden string, such that the adversary cannot get any information about the ciphertext from its description. The security of our scheme is formally analyzed. The proposed scheme provides both confidentiality and anonymity while maintaining its expressiveness. We prove these security properties under the interactive general Diffie–Hellman assumption (i-GDH) and a static assumption introduced in this paper.

Algorithms and Software for Recognition of Address Structures

The article is devoted to the problem of recognizing mail addresses from an arbitrary format string. The purpose of the research is a developing software for automatic mail address recognition in two forms: as a library and as a web server. As an approach to development, object-oriented programming paradigm was used. Preference is given to the C# programming language version 8.0 and ASP.NET Core 3.1 and Entity Framework Core 3.1. Address recognition software has been developed. It can be used as a programming library and as a separate web server with open HTTP REST API. The paper substantiates the need to create software for automating the recognition of address structures from a string of arbitrary format. According to the rules for the contruction of addresses, their basic patterns and nuances are analyzed. During development, fundamentally new mail address recognition algorithms were invented in the C# programming language.

CMB birefringence from ultralight-axion string networks

The polarization of Cosmic Microwave Background (CMB) photons is rotated as they pass through (ultralight-) axion string loops. Studying this birefringence can reveal valuable information about the axion-photon coupling and the structure of the string network. We develop an approximate analytic formalism and identify a kernel function that can be used to calculate the two-point correlation function for CMB birefringence induced by an arbitrary axion string network. Using this formalism, we evaluate the birefringence signal for some simple loop distributions (including scaling and network collapse). We find that the angular correlation function has a characteristic angular scale set by θmin, which corresponds to the angular extent of the loops at the time of recombination. This results in a peak in the birefringence power spectrum around ℓp ∼ 1/θmin. An additional scale, controlled by the axion's mass, is introduced if the network collapses before today.

Chaotic scattering of highly excited strings

Motivated by the desire to understand chaos in the S-matrix of string theory, we study tree level scattering amplitudes involving highly excited strings. While the amplitudes for scattering of light strings have been a hallmark of string theory since its early days, scattering of excited strings has been far less studied. Recent results on black hole chaos, combined with the correspondence principle between black holes and strings, suggest that the amplitudes have a rich structure. We review the procedure by which an excited string is formed by repeatedly scattering photons off of an initial tachyon (the DDF formalism). We compute the scattering amplitude of one arbitrary excited string and any number of tachyons in bosonic string theory. At high energies and high mass excited state these amplitudes are determined by a saddle-point in the integration over the positions of the string vertex operators on the sphere (or the upper half plane), thus yielding a generalization of the “scattering equations”. We find a compact expression for the amplitude of an excited string decaying into two tachyons, and study its properties for a generic excited string. We find the amplitude is highly erratic as a function of both the precise excited string state and of the tachyon scattering angle relative to its polarization, a sign of chaos.

Handwritten Text Recognition using Deep Learning and Word Beam Search

This paper offers a solution to traditional handwriting recognition techniques using concepts of Deep learning and Word Beam Search. This paper explains about how an individual handwritten word is classified from the handwritten text by translating into a digital form. The digital form when trained with the Connectionist Temporal Classification (CTC) loss function, the output produced is a RNN. This is a matrix containing character probabilities for each time-step. The final text is mapped using a CTC decoding algorithm by converting the character probabilities. The recognized text is constructed by a list of words from the dictionary by using the token passing algorithm. It is found the running time of token passing depends on the size of dictionary. Also the numbers like arbitrary character strings will not able to decode. In this paper the decoding search algorithm word beam search is proposed, in order to tackle these types of problems. This methodology support to constrain words similar to those contained in a dictionary. It allows the character strings such as arbitrary non-word between the words, and integrates into a word-level language model. It is found the running time is better when compared with the token passing. The proposed algorithm comprises of the decoding algorithm named vanilla beam search and token passing using the IAM dataset and Bentham data set.

Recent Developments of the Lauricella String Scattering Amplitudes and Their Exact SL(K + 3,C) Symmetry

In this review, we propose a new perspective to demonstrate the Gross conjecture regarding the high-energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSAs) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSAs form an infinite dimensional representation of the SL(K+3,C) group. Moreover, we show that the SL(K+3,C) group can be used to solve all the LSSAs and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove the Gross conjecture, which was previously corrected and proved by the method of the decoupling of zero norm states (ZNS). Finally, the exact LSSA can be used to rederive the recurrence relations of SSA in the Regge scattering limit with associated SL(5,C) symmetry and the extended recurrence relations (including the mass and spin dependent string BCJ relations) in the nonrelativistic scattering limit with the associated SL(4,C) symmetry discovered recently.

Teaching concepts related to finite automata using ComVis

AbstractThis paper describes educational software for visualization and finite automata simulation. The system was developed in Java programming language, and its main purpose is learning process improvement. Using this software, finite automata can be defined in a graphical editor in the form of a state diagram, or by defining the transition function using the transition table. Upon defining an automaton, it is possible to run a visual simulation of the automaton operation for an arbitrary input string, whereby a textual description of the automaton simulation is also obtained. Furthermore, the system allows for conversion of regular expressions to deterministic finite automata and nondeterministic finite automata. The simulation of Thompson's construction algorithm is implemented, so that transformation of a regular expression to the corresponding NFA can be monitored in a step‐by‐step process. The quantitative analysis and evaluation of the effectiveness of the simulator are based on a survey of undergraduate students at two universities. The majority of students found the tool a useful means for better understanding and mastering of finite automata concepts.

A theory of incremental compression

The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can be compressed by searching for those features incrementally, which results in a partition of the information content of the string into a complete set of pairwise independent pieces. The description length of this partition turns out to be close to optimal in terms of the Kolmogorov complexity of the string. Exploiting this decomposition, we introduce ALICE – a computable ALgorithm for Incremental ComprEssion – and derive an expression for its time complexity. Finally, we show that our concept of a feature is closely related to Martin-Löf randomness tests, thereby formalizing the meaning of “property” for computable objects.

SAHA: A String Adaptive Hash Table for Analytical Databases

Hash tables are the fundamental data structure for analytical database workloads, such as aggregation, joining, set filtering and records deduplication. The performance aspects of hash tables differ drastically with respect to what kind of data are being processed or how many inserts, lookups and deletes are constructed. In this paper, we address some common use cases of hash tables: aggregating and joining over arbitrary string data. We designed a new hash table, SAHA, which is tightly integrated with modern analytical databases and optimized for string data with the following advantages: (1) it inlines short strings and saves hash values for long strings only; (2) it uses special memory loading techniques to do quick dispatching and hashing computations; and (3) it utilizes vectorized processing to batch hashing operations. Our evaluation results reveal that SAHA outperforms state-of-the-art hash tables by one to five times in analytical workloads, including Google’s SwissTable and Facebook’s F14Table. It has been merged into the ClickHouse database and shows promising results in production.