On Chomsky Hierarchy of Palindromic Languages

The characterization of the structure of palindromic regular and palindromic context-free languages is described by S. Horváth, J. Karhumäki, and J. Kleijn in 1987. In this paper alternative proofs are given for these characterizations

Optimal alignment algorithm for context-sensitive hidden Markov models

The hidden Markov model is well-known for its efficiency in modeling short-term dependencies between adjacent samples. However, it cannot be used for modeling longer-range interactions between symbols that are distant from each other. In this paper, we introduce the concept of context-sensitive HMM that is capable of modeling strong pairwise correlations between distant symbols. Based on this model, we propose a polynomial-time algorithm that can be used for finding the optimal state sequence of an observed symbol string. The proposed model is especially useful in modeling palindromes, which has an important application in RNA secondary structure analysis

HMM with auxiliary memory: a new tool for modeling RNA structures

For a long time, proteins have been believed to perform most of the important functions in all cells. However, recent results in genomics have revealed that many RNAs that do not encode proteins play crucial roles in the cell machinery. The so-called ncRNA genes that are transcribed into RNAs but not translated into proteins, frequently conserve their secondary structures more than they conserve their primary sequences. Therefore, in order to identify ncRNA genes, we have to take the secondary structure of RNAs into consideration. Traditional approaches that are mainly based on base-composition statistics cannot be used for modeling and identifying such structures and models with more descriptive power are required. In this paper, we introduce the concept of context-sensitive HMMs, which is capable of describing pairwise interactions between distant symbols. It is demonstrated that the proposed model can efficiently model various RNA secondary structures that are frequently observed

The power of writing, a pebble hierarchy and a narrative for the teaching of Automata Theory

In this work we study pebble automata. Those automata constitute an infinite hierarchy of discrete models of computation. The hierarchy begins at the level of finite state automata (0-pebble automata) and approaches the model of onetape Turing machines. Thus, it can be argued that it is a complete hierarchy that covers, in a continuous way, all the models of automata that are important in the theory of computation. We investigate the use of this hierarchy as a narrative for the teaching of automata theory. We also investigate some fundamental questions concerning the power of pebble automata.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Optimal Regular Expressions for Palindromes of Given Length

The language P_n (P?_n, respectively) consists of all words that are palindromes of length 2n (2n-1, respectively) over a fixed binary alphabet. We construct a regular expression that specifies P_n (P?_n, respectively) of alphabetic width 4? 2?-4 (3? 2?-4, respectively) and show that this is optimal, that is, the expression has minimum alphabetic width among all expressions that describe P_n (P?_n, respectively). To this end we give optimal expressions for the first k palindromes in lexicographic order of odd and even length, proving that the optimal bound is 2n+4(k-1)-2 S?(k-1) in case of odd length and 2n+3(k-1)-2 S?(k-1)-1 for even length, respectively. Here S?(n) refers to the Hamming weight function, which denotes the number of ones in the binary expansion of the number n

The power of writing, a pebble hierarchy and a narrative for the teaching of Automata Theory

In this work we study pebble automata. Those automata constitute an infinite hierarchy of discrete models of computation. The hierarchy begins at the level of finite state automata (0-pebble automata) and approaches the model of onetape Turing machines. Thus, it can be argued that it is a complete hierarchy that covers, in a continuous way, all the models of automata that are important in the theory of computation. We investigate the use of this hierarchy as a narrative for the teaching of automata theory. We also investigate some fundamental questions concerning the power of pebble automata.Sociedad Argentina de Informática e Investigación Operativa (SADIO