Construction of minimal DFAs from biological motifs

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple non-deterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs can be constructed from two types of patterns popular in bioinformatics, namely (sets of) generalized strings and (generalized) strings with a Hamming neighborhood

On the bit-parallel simulation of the nondeterministic Aho-Corasick and suffix automata for a set of patterns

In this paper we present a method to simulate, using the bit-parallelism technique, the nondeterministic Aho-Corasick automaton and the nondeterministic suffix automaton induced by the trie and by the Directed Acyclic Word Graph for a set of patterns, respectively. When the prefix redundancy is nonnegligible, this method yields-if compared to the original bit-parallel encoding with no prefix factorization-a representation that requires smaller bit-vectors and, correspondingly, less words. In particular, if we restrict to single-word bit-vectors, more patterns can be packed into a word. We also present two simple algorithms, based on such a technique, for searching a set P of patterns in a text T of length n over an alphabet @S of size @s. Our algorithms, named Log-And and Backward-Log-And, require O(([email protected])@?m/[email protected]?)-space, and work in O([email protected]?m/[email protected]?) and O([email protected]?m/[email protected]?l"m"i"n) worst-case searching time, respectively, where w is the number of bits in a computer word, m is the number of states of the automaton, and l"m"i"n is the length of the shortest pattern in P

DNA ANALYSIS USING GRAMMATICAL INFERENCE

An accurate language definition capable of distinguishing between coding and non-coding DNA has important applications and analytical significance to the field of computational biology. The method proposed here uses positive sample grammatical inference and statistical information to infer languages for coding DNA. An algorithm is proposed for the searching of an optimal subset of input sequences for the inference of regular grammars by optimizing a relevant accuracy metric. The algorithm does not guarantee the finding of the optimal subset; however, testing shows improvement in accuracy and performance over the basis algorithm. Testing shows that the accuracy of inferred languages for components of DNA are consistently accurate. By using the proposed algorithm languages are inferred for coding DNA with average conditional probability over 80%. This reveals that languages for components of DNA can be inferred and are useful independent of the process that created them. These languages can then be analyzed or used for other tasks in computational biology. To illustrate potential applications of regular grammars for DNA components, an inferred language for exon sequences is applied as post processing to Hidden Markov exon prediction to reduce the number of wrong exons detected and improve the specificity of the model significantly

Fuzzy Automata: A Quantitative Review

Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and many more. In this paper, a methodical literature review is carried out on various research works in the field of Fuzzy automata and explained the challenging issues in the field of fuzzy automata

Tree pattern matching from regular tree expressions

summary:In this work we deal with tree pattern matching over ranked trees, where the pattern set to be matched against is defined by a regular tree expression. We present a new method that uses a tree automaton constructed inductively from a regular tree expression. First we construct a special tree automaton for the regular tree expression of the pattern $E$, which is somehow a generalization of Thompson automaton for strings. Then we run the constructed automaton on the subject tree $t$. The pattern matching algorithm requires an $\mathcal{O}(\vert t\vert\vert E\vert)$ time complexity, where $\vert t\vert$ is the number of nodes of $t$ and $\vert E\vert$ is the size of the regular tree expression $E$. The novelty of this contribution besides the low time complexity is that the set of patterns can be infinite, since we use regular tree expressions to represent patterns

Streaming Tree Transducers

Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output in linear time using a finite-state control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of string-concatenation and tree-insertion. We prove that the expressiveness of the model coincides with transductions definable using monadic second-order logic (MSO). Existing models of tree transducers either cannot implement all MSO-definable transformations, or require regular look ahead that prohibits single-pass implementation. We show a variety of analysis problems such as type-checking and checking functional equivalence are solvable for our model.Comment: 40 page

Compressed Full-Text Indexes for Highly Repetitive Collections

This thesis studies problems related to compressed full-text indexes. A full-text index is a data structure for indexing textual (sequence) data, so that the occurrences of any query string in the data can be found efficiently. While most full-text indexes require much more space than the sequences they index, recent compressed indexes have overcome this limitation. These compressed indexes combine a compressed representation of the index with some extra information that allows decompressing any part of the data efficiently. This way, they provide similar functionality as the uncompressed indexes, while using only slightly more space than the compressed data. The efficiency of data compression is usually measured in terms of entropy. While entropy-based estimates predict the compressed size of most texts accurately, they fail with highly repetitive collections of texts. Examples of such collections include different versions of a document and the genomes of a number of individuals from the same population. While the entropy of a highly repetitive collection is usually similar to that of a text of the same kind, the collection can often be compressed much better than the entropy-based estimate. Most compressed full-text indexes are based on the Burrows-Wheeler transform (BWT). Originally intended for data compression, the BWT has deep connections with full-text indexes such as the suffix tree and the suffix array. With some additional information, these indexes can be simulated with the Burrows-Wheeler transform. The first contribution of this thesis is the first BWT-based index that can compress highly repetitive collections efficiently. Compressed indexes allow us to handle much larger data sets than the corresponding uncompressed indexes. To take full advantage of this, we need algorithms for constructing the compressed index directly, instead of first constructing an uncompressed index and then compressing it. The second contribution of this thesis is an algorithm for merging the BWT-based indexes of two text collections. By using this algorithm, we can derive better space-efficient construction algorithms for BWT-based indexes. The basic BWT-based indexes provide similar functionality as the suffix array. With some additional structures, the functionality can be extended to that of the suffix tree. One of the structures is an array storing the lengths of the longest common prefixes of lexicographically adjacent suffixes of the text. The third contribution of this thesis is a space-efficient algorithm for constructing this array, and a new compressed representation of the array. In the case of individual genomes, the highly repetitive collection can be considered a sample from a larger collection. This collection consists of a reference sequence and a set of possible differences from the reference, so that each sequence contains a subset of the differences. The fourth contribution of this thesis is a BWT-based index that extrapolates the larger collection from the sample and indexes it.Tässä väitöskirjassa käsitellään tiivistettyjä kokotekstihakemistoja tekstimuotoisille aineistoille. Kokotekstihakemistot ovat tietorakenteita, jotka mahdollistavat mielivaltaisten hahmojen esiintymien löytämisen tekstistä tehokkaasti. Perinteiset kokotekstihakemistot, kuten loppuosapuut ja -taulukot, vievät moninkertaisesti tilaa itse aineistoon nähden. Viime aikoina on kuitenkin kehitetty tiivistettyjä hakemistorakenteita, jotka tarjoavat vastaavan toiminnallisuuden alkuperäistä tekstiä pienemmässä tilassa. Tämä on mahdollistanut aikaisempaa suurempien aineistojen käsittelyn. Tekstin tiivistyvyyttä mitataan yleensä suhteessa sen entropiaan. Vaikka entropiaan perustuvat arviot ovat useimmilla aineistoilla varsin tarkkoja, aliarvioivat ne vahvasti toisteisien aineistojen tiivistyvyyttä. Esimerkkejä tällaisista aineistoista ovat kokoelmat saman populaation yksilöiden genomeita tai saman dokumentin eri versioita. Siinä missä tällaisen kokoelman entropia suhteessa aineiston kokoon on vastaava kuin yksittäisellä samaa tyyppiä olevalla tekstillä, tiivistyy kokoelma yleensä huomattavasti paremmin kuin entropian perusteella voisi odottaa. Useimmat tiivistetyt kokotekstihakemistot perustuvat Burrows-Wheeler-muunnokseen (BWT), joka kehitettiin alun perin tekstimuotoisten aineistojen tiivistämiseen. Pian kuitenkin havaittiin, että koska BWT muistuttaa rakenteeltaan loppuosapuuta ja -taulukkoa, voidaan sitä käyttää niissä tehtävien hakujen simulointiin. Tässä väitöskirjassa esitetään ensimmäinen BWT-pohjainen kokotekstihakemisto, joka pystyy tiivistämään vahvasti toisteiset aineistot tehokkaasti. Tiivistettyjen tietorakenteiden käyttö mahdollistaa suurempien aineistoiden käsittelemisen kuin tavallisia tietorakenteita käytettäessä. Tämä etu kuitenkin menetetään, jos tiivistetty tietorakenne muodostetaan luomalla ensin vastaava tavallinen tietorakenne ja tiivistämällä se. Tässä väitöskirjassa esitetään aikaisempaa vähemmän muistia käyttäviä algoritmeja BWT-pohjaisten kokotekstihakemistojen muodostamiseen. Kokoelma yksilöiden genomeita voidaan käsittää otokseksi suuremmasta kokoelmasta, joka koostuu populaation kaikkien yksilöiden sekä niiden hypoteettisten jälkeläisten genomeista. Tällainen kokoelma voidaan esittää äärellisenä automaattina, joka muodostuu referenssigenomista ja yksilöiden genomeissa esiintyvistä poikkeamista referenssistä. Tässä väitöskirjassa esitetään BWT-pohjaisten kokotekstihakemistojen yleistys, joka mahdollistaa tällaisten automaattien indeksoinnin