Regular Combinators for String Transformations

We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way finite-state transducers, (one-way) cost register automata, and MSO-definable graph transformations. In this paper, we give an algebraic and machine-independent characterization of this class analogous to the definition of regular languages by regular expressions. When the monoid is commutative, we prove that every regular function can be constructed from constant functions using the combinators of choice, split sum, and iterated sum, that are analogs of union, concatenation, and Kleene-*, respectively, but enforce unique (or unambiguous) parsing. Our main result is for the general case of non-commutative monoids, which is of particular interest for capturing regular string-to-string transformations for document processing. We prove that the following additional combinators suffice for constructing all regular functions: (1) the left-additive versions of split sum and iterated sum, which allow transformations such as string reversal; (2) sum of functions, which allows transformations such as copying of strings; and (3) function composition, or alternatively, a new concept of chained sum, which allows output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of the conference paper currently in submissio

Performance Analysis of the SHA-3 Candidates on Exotic Multi-core Architectures

The NIST hash function competition to design a new cryptographic hash standard 'SHA-3' is currently one of the hot topics in cryptologic research, its outcome heavily depends on the public evaluation of the remaining 14 candidates. There have been several cryptanalytic efforts to evaluate the security of these hash functions. Concurrently, invaluable benchmarking efforts have been made to measure the performance of the candidates on multiple architectures. In this paper we contribute to the latter; we evaluate the performance of all second-round SHA-3 candidates on two exotic platforms: the Cell Broadband Engine (Cell) and the NVIDIA Graphics Processing Units (GPUs). Firstly, we give performance estimates for each candidate based on the number of arithmetic instructions, which can be used as a starting point for evaluating the performance of the SHA-3 candidates on various platforms. Secondly, we use these generic estimates and Cell-/GPU-specific optimization techniques to give more precise figures for our target platforms, and finally, we present implementation results of all 10 non-AES based SHA-3 candidates

Pumping lemma and Ogden lemma for displacement context-free grammars

The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiple-context free languages. However, the statement of lemma is too weak for practical usage. We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for this language family. We also use these statements to prove that some natural context-sensitive languages cannot be generated by tree-adjoining grammars.Comment: Shortened version accepted to DLT 2014 conferenc

Maintenance of metaphase chromosome architecture by condensin I

"Faithful segregation of the genome into two daughter cells is one of the most fundamental events for every living organism. In each round of the cell cycle, cells need to orchestrate a sequence of complex steps to replicate their genetic material, pack it neatly into mitotic chromosomes and perform their precise separation when all the prerequisites are met. One of the most fascinating questions in biology is to understand the internal organization of mitotic chromosomes. Even though mitotic chromosomes were first described around 140 years ago, how exactly interphase DNA molecules are packed to become mitotic chromosomes is still a mystery. Despite the lack of precise details about chromosome condensation mechanisms, it is believed that in the heart of this process lies a group of protein complexes called condensins. The mechanism by which condensins are able to enforce or guide the condensation process is yet unknown. In this thesis, we will present our advances in understanding condensin’s function in maintaining mitotic chromosome compaction and internal architecture.(...)

Boundedness in languages of infinite words

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions where two new variants of the Kleene star $L^*$ are added: $L^B$ and $L^S$. These new exponents are used to say that parts of the input word have bounded size, and that parts of the input can have arbitrarily large sizes, respectively. For instance, the expression $(a^Bb)^\omega$ represents the language of infinite words over the letters $a,b$ where there is a common bound on the number of consecutive letters $a$. The expression $(a^Sb)^\omega$ represents a similar language, but this time the distance between consecutive $b$'s is required to tend toward the infinite. We develop a theory for these languages, with a focus on decidability and closure. We define an equivalent automaton model, extending B\"uchi automata. The main technical result is a complementation lemma that works for languages where only one type of exponent---either $L^B$ or $L^S$---is used. We use the closure and decidability results to obtain partial decidability results for the logic MSOLB, a logic obtained by extending monadic second-order logic with new quantifiers that speak about the size of sets

G-Merkle: A Hash-Based Group Signature Scheme From Standard Assumptions

Hash-based signature schemes are the most promising cryptosystem candidates in a post-quantum world, but offer little structure to enable more sophisticated constructions such as group signatures. Group signatures allow a group member to anonymously sign messages on behalf of the whole group (as needed for anonymous remote attestation). In this work, we introduce G-Merkle, the first (stateful) hash-based group signature scheme. Our proposal relies on minimal assumptions, namely the existence of one-way functions, and offers performance equivalent to the Merkle single-signer setting. The public key size (as small as in the single-signer setting) outperforms all other post-quantum group signatures. Moreover, for $N$ group members issuing at most $B$ signatures each, the size of a hash-based group signature is just as large as a Merkle signature with a tree composed by $N\cdot B$ leaf nodes. This directly translates into fast signing and verification engines. Different from lattice-based counterparts, our construction does not require any random oracle. Note that due to the randomized structure of our Merkle tree, the signature authentication paths are pre-stored or deduced from a public tree, which seems a requirement hard to circumvent. To conclude, we present implementation results to demonstrate the practicality of our proposal

Varieties of Signature Tensors

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures.Comment: 52 pages, 1 figure, 6 tables; to appear in Forum of Mathematics, Sigm

On the Derivative of 2-Holonomy for a Non-Abelian Gerbe

The local 2-holonomy for a non abelian gerbe with connection is first studied via a local zig-zag Hochschild complex. Next, by locally integrating the cocycle data for our gerbe with connection, and then glueing this data together, an explicit definition is offered for a global version of 2-holonomy. After showing this definition satisfies the desired properties for 2-holonomy, its derivative is calculated whereby the only interior information added is the integration of the 3-curvature. Finally, for the case when the surface being mapped into the manifold is a sphere, the derivative of 2-holonomy is extended to an equivariant closed form in the spirit of the construction of Tradler-Wilson-Zeinalian for abelian gerbes