Da-Jung Cho

Alignment with Non-overlapping Inversions on Two Strings

The inversion is one of the important operations in bio sequence analysis and the sequence alignment problem is well-studied for efficient bio sequence comparisons. Based on inversion operations, we introduce the alignment with non-overlapping inversion problem: Given two strings x and y, does there exist an alignment with non-overlapping inversions for x and y. We, in particular, consider the alignment problem when non-overlapping inversions are allowed for both x and y. We design an efficient algorithm that determines the existence of non-overlapping inversions and present another efficient algorithm that retrieves such an alignment, if exists.

Pseudo-inversion on Formal Languages

We consider the pseudo-inversion operation inspired by a biological event as a result of the partial inversion. We define the pseudo-inversion of a string w = uxv to consist of all strings v R xu R , where uv ≠ λ and consider the operation from a formal language theoretic viewpoint. We show that regular languages are closed under the pseudo-inversion operation whereas context-free languages are not. Furthermore, we consider the iterated pseudo-inversion operation and establish the basic properties. Finally, we introduce the pseudo-inversion-freeness and examine closure properties and decidability problems for regular and context-free languages. We establish that pseudo-inversion-freeness is decidable in polynomial time for regular languages and undecidable for context-free languages.

Alignment with non-overlapping inversions and translocations on two strings

An inversion and a translocation are important in bio sequence analysis and motivate researchers to consider the sequence alignment problem using these operations. Based on inversion and translocation, we introduce a new alignment problem with non-overlapping inversions and translocations-given two strings x and y, find an alignment with non-overlapping inversions and translocations for x and y. This problem has interesting application for finding a common sequence from two mutated sequences. We, in particular, consider the alignment problem when non-overlapping inversions and translocations are allowed for both x and y. We design an efficient algorithm that determines the existence of such an alignment and retrieves an alignment, if exists.

State complexity of permutation on finite languages over a binary alphabet

Abstract The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with n 2 − n + 2 2 states. We show that if the language consists of equal length binary strings the bound can be improved to f ( n ) = n 2 + n + 1 3 and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L ( A ) needs f ( n ) states.

State complexity of inversion operations

The reversal operation is well-studied in the literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2 n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion (respectively, prefix-inversion) of a language L consists of all strings u x R v such that u x v ? L (respectively, all strings u R x where u x ? L ). We show that the nondeterministic state complexity of prefix-inversion is ? ( n 2 ) and that of inversion is ? ( n 3 ) . We show that the deterministic state complexity of prefix-inversion is at most 2 n ? log ? n + n and has lower bound 2 ? ( n log ? n ) . The same lower bound holds for the state complexity of inversion, but for inversion we do not have a matching upper bound. We also study the state complexity of other variants of the inversion operation.

Frequent Pattern Mining with Non-overlapping Inversions

Frequent pattern mining is widely used in bioinformatics since frequent patterns in bio sequences often correspond to residues conserved during evolution. In bio sequence analysis, non-overlapping inversions are well-studied because of their practical properties for local sequence comparisons. We consider the problem of finding frequent patterns in a bio sequence with respect to non-overlapping inversions, and design efficient algorithms.

Decidability of involution hypercodes

Given a finite set X of strings, X is a hypercode if a string in X is not a subsequence of any other string in X. We consider hypercodes for involution codes, which are useful for DNA strand design, and define an involution hypercode. We then tackle the involution hypercode decidability problem; that is, to determine whether or not a given language is an involution hypercode. Based on the hypercode properties, we design a polynomial runtime algorithm for regular languages. We also prove that it is decidable whether or not a context-free language is an involution hypercode. Note that it is undecidable for some other involution codes such as involution prefix codes, suffix codes, and k-intercodes.

Site-Directed Deletion

We introduce a new bio-inspired operation called a site-directed deletion motivated from site-directed mutagenesis performed by enzymatic activity of DNA polymerase: Given two strings x and y, a site-directed deletion partially deletes a substring of x guided by the string y that specifies which part of a substring can be deleted. We study a few decision problems with respect to the new operation and examine the closure properties of the (iterated) site-directed deletion operations. We, then, define a site-directed deletion-closed (and -free) language L and investigate its decidability properties when L is regular or context-free.

Pseudoknot-Generating Operation

A pseudoknot is an intra-molecular structure formed primarily in RNA strands and much research has been done to predict efficiently pseudoknot structures in RNA. We define an operation that generates all pseudoknots from a given sequence and consider algorithmic and language theoretic properties of the operation. We give an efficient algorithm to decide whether a given string is a pseudoknot of a regular language L--the runtime is linear if L is given by a deterministic finite automaton. We consider closure and decision properties of the pseudoknot-generating operation. For DNA encoding applications, pseudoknot structures are undesirable. We give polynomial-time algorithms to decide whether a regular language L contains a pseudoknot or a pseudoknot generated by some string of L. Furthermore, we show that the corresponding questions for context-free languages are undecidable.

Duplications and Pseudo-Duplications

A duplication is basic phenomenon that occurs through molecular evolution on a biological sequence. A duplication on a string copies any substring of the string. We define k-pseudo-duplication of a string w that consists, roughly speaking, of all strings obtained from w by inserting after a substring u another substring obtained from u by at most k edit operations. We consider three variants of duplication operations, duplication, k-pseudo-duplication and reverse-duplication. First, we give the necessary and sufficient number of states that a nondeterministic finite automaton needs to recognize duplications on a string. Then, we show that regular languages and context-free languages are not closed under the duplication, k-pseudo-duplication and reverse-duplication operations. Furthermore, we show that the class of context-sensitive languages is closed under duplication, pseudo-duplication and reverse-duplication.