Quantum, Stochastic, and Pseudo Stochastic Languages with Few States

Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal. After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata. Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power.Comment: A new version with new results. Previous version: Arseny M. Shur, Abuzer Yakaryilmaz: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. UCNC 2014: 327-33

Real-Time Vector Automata

We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.Comment: 14 page

Scalar Ambiguity and Freeness in Matrix Semigroups over Bounded Languages

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, mainly related to the dimensions of the generator matrices and the semiring over which the matrices are defined. A recent paper has also investigated freeness properties of matrices within a bounded language of matrices, which are of the form M1M2 · · · Mk ⊆ F n×n for some semiring F [9]. Most freeness problems have been shown to be undecidable starting from dimension three, even for upper-triangular matrices over the natural numbers. There are many open problems still remaining in dimension two. We introduce a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρ TMτ |M ∈ S}, where ρ, τ ∈ F n are vectors and S is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of uniqueness of factorizations leading to each scalar. We show various undecidability results

Phenotypic and genotypic diversity of wine yeasts used for acidic musts

The aim of this study was to examine the physiological and genetic stability of the industrial wine yeasts Saccharomyces cerevisiae and Saccharomyces bayanus var. uvarum under acidic stress during fermentation. The yeasts were sub-cultured in aerobic or fermentative conditions in media with or without l-malic acid. Changes in the biochemical profiles, karyotypes, and mitochondrial DNA profiles were assessed after minimum 50 generations. All yeast segregates showed a tendency to increase the range of compounds used as sole carbon sources. The wild strains and their segregates were aneuploidal or diploidal. One of the four strains of S. cerevisiae did not reveal any changes in the electrophoretic profiles of chromosomal and mitochondrial DNA, irrespective of culture conditions. The extent of genomic changes in the other yeasts was strain-dependent. In the karyotypes of the segregates, the loss of up to 2 and the appearance up to 3 bands was noted. The changes in their mtDNA patterns were much broader, reaching 5 missing and 10 additional bands. The only exception was S. bayanus var. uvarum Y.00779, characterized by significantly greater genome plasticity only under fermentative stress. Changes in karyotypes and mtDNA profiles prove that fermentative stress is the main driving force of the adaptive evolution of the yeasts. l-malic acid does not influence the extent of genomic changes and the resistance of wine yeasts exhibiting increased demalication activity to acidic stress is rather related to their ability to decompose this acid. The phenotypic changes in segregates, which were found even in yeasts that did not reveal deviations in their DNA profiles, show that phenotypic characterization may be misleading in wine yeast identification. Because of yeast gross genomic diversity, karyotyping even though it does not seem to be a good discriminative tool, can be useful in determining the stability of wine yeasts. Restriction analysis of mitochondrial DNA appears to be a more sensitive method allowing for an early detection of genotypic changes in yeasts. Thus, if both of these methods are applied, it is possible to conduct the quick routine assessment of wine yeast stability in pure culture collections depositing industrial strains

Application of the bacteriophage Mu-driven system for the integration/amplification of target genes in the chromosomes of engineered Gram-negative bacteria—mini review

The advantages of phage Mu transposition-based systems for the chromosomal editing of plasmid-less strains are reviewed. The cis and trans requirements for Mu phage-mediated transposition, which include the L/R ends of the Mu DNA, the transposition factors MuA and MuB, and the cis/trans functioning of the E element as an enhancer, are presented. Mini-Mu(LR)/(LER) units are Mu derivatives that lack most of the Mu genes but contain the L/R ends or a properly arranged E element in cis to the L/R ends. The dual-component system, which consists of an integrative plasmid with a mini-Mu and an easily eliminated helper plasmid encoding inducible transposition factors, is described in detail as a tool for the integration/amplification of recombinant DNAs. This chromosomal editing method is based on replicative transposition through the formation of a cointegrate that can be resolved in a recombination-dependent manner. (E-plus)- or (E-minus)-helpers that differ in the presence of the trans-acting E element are used to achieve the proper mini-Mu transposition intensity. The systems that have been developed for the construction of stably maintained mini-Mu multi-integrant strains of Escherichia coli and Methylophilus methylotrophus are described. A novel integration/amplification/fixation strategy is proposed for consecutive independent replicative transpositions of different mini-Mu(LER) units with “excisable” E elements in methylotrophic cells

Transposition-based method for the rapid generation of gene-targeting vectors to produce Cre/Flp-modifiable conditional knock-out mice

Peer reviewe

Theory of one tape linear time Turing machines

Abstract. A theory of one-tape linear-time Turing machines is quite different from its polynomial-time counterpart. This paper discusses the computational complexity of one-tape Turing machines of various machine types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in time O(n), where the running time of a machine is defined as the height of its computation tree. We also address a close connection between one-tape linear-time Turing machines and finite state automata. §1. Model of Computation: Turing Machines. We use a standard definition of an off-line Turing machine. Of special interest is a one-tape Turing machine (abbreviated 1TM) M = (Q, Σ, Γ, δ, q0, qacc, qrej), where Q is a finite set of (internal) states, Σ is a nonempty finite input alphabet 3, Γ is a finite tape alphabet including Σ, q0 in Q is an initial state, qacc and qrej in Q are an accepting state and a rejecting state, respectively, and δ is a transition function. Different transition functions δ give rise to various types of 1TMs described i