887 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
The brown algal genus Fucus : A unique insight into reproduction and the evolution of sex-biased genes
Doctoral thesis (PhD) - Nord University, 2023publishedVersio
Prefix monoids of groups and right units of special inverse monoids
A prefix monoid is a finitely generated submonoid of a finitely presented
group generated by the prefixes of its defining relators. Important results of
Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word
problem for certain one-relator monoids, and inverse monoids, can be reduced to
solving the membership problem in prefix monoids of certain one-relator groups.
Motivated by this, in this paper we study the class of prefix monoids of
finitely presented groups. We obtain a complete description of this class of
monoids. All monoids in this family are finitely generated, recursively
presented and group-embeddable. Our results show that not every finitely
generated recursively presented group-embeddable monoid is a prefix monoid, but
for every such monoid if we take a free product with a suitably chosen free
monoid of finite rank, then we do obtain a prefix monoid. Conversely we prove
that every prefix monoid arises in this way. Also, we show that the groups that
arise as groups of units of prefix monoids are precisely the finitely generated
recursively presented groups, while the groups that arise as Sch\"utzenberger
groups of prefix monoids are exactly the recursively enumerable subgroups of
finitely presented groups. We obtain an analogous result classifying the
Sch\"utzenberger groups of monoids of right units of special inverse monoids.
We also give some examples of right cancellative monoids arising as monoids of
right units of finitely presented special inverse monoids, and show that not
all right cancellative recursively presented monoids belong to this class.Comment: 22 page
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Finite group lattice gauge theories for quantum simulation
The present manuscript focuses on Lattice Gauge Theories based on finite groups. For the purpose of Quantum Simulation, the Hamiltonian approach is considered, while the finite group serves as a discretization scheme for the degrees of freedom of the gauge fields. Several aspects of these models are studied. First, we investigate dualities in Abelian models with a restricted geometry, using a systematic approach. This leads to a rich phase diagram dependent on the super-selection sectors. Second, we construct a family of lattice Hamiltonians for gauge theories with a finite group, either Abelian or non-Abelian. We show that is possible to express the electric term as a natural graph Laplacian, and that the physical Hilbert space can be explicitly built using spin network states. In both cases we perform numerical simulations in order to establish the correctness of the theoretical results and further investigate the models
Decryption Failure Attacks on Post-Quantum Cryptography
This dissertation discusses mainly new cryptanalytical results related to issues of securely implementing the next generation of asymmetric cryptography, or Public-Key Cryptography (PKC).PKC, as it has been deployed until today, depends heavily on the integer factorization and the discrete logarithm problems.Unfortunately, it has been well-known since the mid-90s, that these mathematical problems can be solved due to Peter Shor's algorithm for quantum computers, which achieves the answers in polynomial time.The recently accelerated pace of R&D towards quantum computers, eventually of sufficient size and power to threaten cryptography, has led the crypto research community towards a major shift of focus.A project towards standardization of Post-quantum Cryptography (PQC) was launched by the US-based standardization organization, NIST. PQC is the name given to algorithms designed for running on classical hardware/software whilst being resistant to attacks from quantum computers.PQC is well suited for replacing the current asymmetric schemes.A primary motivation for the project is to guide publicly available research toward the singular goal of finding weaknesses in the proposed next generation of PKC.For public key encryption (PKE) or digital signature (DS) schemes to be considered secure they must be shown to rely heavily on well-known mathematical problems with theoretical proofs of security under established models, such as indistinguishability under chosen ciphertext attack (IND-CCA).Also, they must withstand serious attack attempts by well-renowned cryptographers both concerning theoretical security and the actual software/hardware instantiations.It is well-known that security models, such as IND-CCA, are not designed to capture the intricacies of inner-state leakages.Such leakages are named side-channels, which is currently a major topic of interest in the NIST PQC project.This dissertation focuses on two things, in general:1) how does the low but non-zero probability of decryption failures affect the cryptanalysis of these new PQC candidates?And 2) how might side-channel vulnerabilities inadvertently be introduced when going from theory to the practice of software/hardware implementations?Of main concern are PQC algorithms based on lattice theory and coding theory.The primary contributions are the discovery of novel decryption failure side-channel attacks, improvements on existing attacks, an alternative implementation to a part of a PQC scheme, and some more theoretical cryptanalytical results
A profinite approach to complete bifix decodings of recurrent languages
We approach the study of complete bifix decodings of (uniformly) recurrent
languages with the help of the free profinite monoid. We show that the complete
bifix decoding of a uniformly recurrent language by an -charged rational
complete bifix code is uniformly recurrent. An analogous result is obtained for
recurrent languages.Comment: Original Manuscript of article to be published by De Gruyter in Forum
Mathematicum. The last section of the version in Forum Mathematicum is very
different, as there it is not proved that the Sch\"utzenberger group is an
invariant of eventual conjugacy (the argument in the Original Manuscript had
a flaw), but only that its maximal pronilpotent quotient is invariant by
eventual conjugac
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