Language equations, maximality and error-detection

Kari, Lila; Konstantinidis, Stavros

doi:10.1016/j.jcss.2004.08.005

Cited by 13 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By utilizing and improving recent results in [9] on language inequations, we furthermore show that for many of the bond-free properties the maximality problem is decidable. Polynomial-time algorithms are presented for the case of θ-compliant finite sets and θ-non-overlapping regular sets.…”

Section: Introductionmentioning

confidence: 66%

See 1 more Smart Citation

Preventing Undesirable Bonds Between DNA Codewords

2005

Self Cite

View full text Add to dashboard Cite

Abstract. The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a double-stranded DNA sequence, one has to impose restrictions on these sets of DNA words (=languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.

show abstract

Section: Introductionmentioning

confidence: 66%

“…The symbol M ⊆ Σ * represents the set of all applicable/constructible DNA strands in a case at hand. The following theorem is based on nontrivial results concerning language inequations in [9].…”

Section: Maximal Bond-free Languagesmentioning

confidence: 99%

Preventing Undesirable Bonds Between DNA Codewords

2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let us show that the resulting system (13), (8) , (14) which consists of multiple pairwise incomparable vectors of languages. This shows the correctness of the reduction and proves Π 2 -hardness.…”

Section: Claim 3 L I L I+1 For All Imentioning

confidence: 99%

Decision problems for language equations

Okhotin¹

2010

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Equations with formal languages as unknowns using all Boolean operations and concatenation are studied. Their main properties, such as solution existence and uniqueness, are characterized by first-order formulae. It is shown that testing solution existence is Π 1 -complete, while solution uniqueness and existence of a least and of a greatest solution are all Π 2 -complete problems. The families of languages defined by components of unique, least and greatest solutions of such systems are shown to coincide with the classes of recursive, recursively enumerable and co-recursively enumerable sets, respectively.

show abstract

“…Thus, a code property P t is defined via a certain kind of transducer t which can be used to effectively provide the property as input to a decision algorithm. We note that the transducer-based approach stems from the ideas in [8] where a code property is defined via a language equation involving a word operation.…”

Section: Introductionmentioning

confidence: 99%

On the maximality of languages with combined types of code properties

Kari

Konstantinidis

Kopecki

2014

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

We consider the decision problem of whether or not a given regular language is maximal with respect to certain combined types of code properties. In the recent past, there have been a few formal methods for defining code properties, such as trajectory-based codes and transducer-based codes, that allow one to decide the maximality problem, including the case where maximality is tested with respect to combined properties within these formal methods. The property of "decoding delay 1" is not known to be definable with these methods, but it is known that the maximality of this property alone is decidable for regular languages. Here, we consider the problem of deciding maximality of a regular language with respect to decoding delay 1 and a transducer-based property, such as suffix-free, overlap-free, and error-detection properties.

show abstract

Language equations, maximality and error-detection

Cited by 13 publications

References 12 publications

Preventing Undesirable Bonds Between DNA Codewords

Preventing Undesirable Bonds Between DNA Codewords

Decision problems for language equations

On the maximality of languages with combined types of code properties

Contact Info

Product

Resources

About