Acta Informatica最新文献

Let K and L be two languages over (Sigma ) and (Gamma ) (with (Gamma subset Sigma )), respectively. Then, the L-reduction of K, denoted by (K%,L), is defined by ({ u_0u_1cdots u_n in (Sigma - Gamma )^* mid u_0v_1u_1 cdots v_nu_n in K, v_i in L (1le i le n) }). This is extended to language classes as follows: ({mathcal {K}}% {mathcal {L}}={K%L mid K in {mathcal {K}}, , L in {mathcal {L}} }). In this paper, we investigate the computing powers of (mathcal {K}%,mathcal {L}) in which (mathcal {K}) ranges among various classes of (mathcal {INS}^i_{!!j}) and min-(mathcal {LIN}), while (mathcal {L}) is taken as (mathcal {DYCK}) and (mathcal {F}), where (mathcal {INS}^i_{!!j}): the class of insertion languages of weight (j, i), min-(mathcal {LIN}): the class of minimal linear languages, (mathcal {DYCK}): the class of Dyck languages, and (mathcal {F}): the class of finite languages. The obtained results include:

• (mathcal {INS}^1_1,%,mathcal {DYCK}=mathcal {RE})

• (mathcal {INS}^0_i,%,mathcal {F}= mathcal {INS}^1_j,%,mathcal {F}=mathcal {CF}) (for (ige 3) and (jge 1))

• (mathcal {INS}^0_2,%,mathcal {DYCK}=mathcal {INS}^0_2)

• min-(mathcal {LIN},%,mathcal {F}_1=mathcal {LIN})

where (mathcal {RE}), (mathcal {CF}), (mathcal {LIN}), (mathcal {F}_1) are classes of recursively enumerable, of context-free, of linear languages, and of singleton languages over unary alphabet, respectively. Further, we provide a very simple alternative proof for the known result min-(mathcal {LIN},%,mathcal {DYCK}_2=mathcal {RE}). We also show that with a certain condition, for the class of context-sensitive languages (mathcal {CS}), there exists no (mathcal {K}) such that (mathcal {K}%,mathcal {DYCK}=mathcal {CS}), which is in marked contrast to the characterization results mentioned above for other classes in Chomsky hierarchy. It should be remarked from the viewpoint of molecular computing theory that the notion of L-reduction is naturally motivated by a molecular biological functioning well-known as RNA splicing occurring in most eukaryotic genes.

The minimum status (or its normalized version called proximity) is a well-known concept in communication network theory. We determine the trees minimizing the minimum status among trees with a given degree sequence, and we show that the trees maximizing the minimum status among trees with a given degree sequence must be caterpillars with specific properties.

Huang and Wong (Acta Inform 21(1):113–123, 1984) proposed a polynomial-time dynamic-programming algorithm for computing optimal generalized binary split trees. We show that their algorithm is incorrect. Thus, it remains open whether such trees can be computed in polynomial time. Spuler (Optimal search trees using two-way key comparisons, PhD thesis, 1994) proposed modifying Huang and Wong’s algorithm to obtain an algorithm for a different problem: computing optimal two-way comparison search trees. We show that the dynamic program underlying Spuler’s algorithm is not valid, in that it does not satisfy the necessary optimal-substructure property and its proposed recurrence relation is incorrect. It remains unknown whether the algorithm is guaranteed to compute a correct overall solution.

Jumping finite automata and sensing (5'rightarrow 3') Watson–Crick finite automata are finite-state models of computation which allow to process the input word not only in the strictly left-to-right manner. In this paper a new combined model of them is presented. The accepting power of the new model is studied and compared with the original models and also other well-known language families. Furthermore, the paper investigates changes in the accepting power when commonly studied restrictions from Watson–Crick finite automata, e.g., all states are final, are applied to this combined model. In the end, the paper presents a comprehensive hierarchy of all related language families.

Biclustering is a two-dimensional data analysis technique that, applied to a matrix, searches for a subset of rows and columns that intersect to produce a submatrix with given, expected features. Such an approach requires different methods to those of typical classification or regression tasks. In recent years it has become possible to express biclustering goals in the form of Boolean reasoning. This paper presents a new, heuristic approach to bicluster induction in binary data.

For each two-way alternating finite automaton (a fa) A with s states, we directly build a a fa (A^c ) with (O(s^6)) states which accepts exactly those inputs that are not accepted by A. This improves upon the previously best-known construction, which was both more expensive and more complicated, as it required (O(s^7)) states and involved building and simulating an intermediate linear-bounded automaton.

Transforming (omega )-automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches.