Acta Informatica最新文献

Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to neighboring instances. We combine both techniques, in order to better classify the complexity of problems in the parameterized setting. Specifically, we see that some problems in the class of compositional problems, which do not have polynomial kernels under standard complexity-theoretic assumptions, do have polynomial kernels under the reoptimization model for some local modifications. We also observe that, for some other local modifications, these same problems do not have polynomial kernels unless (mathbf{NP}subseteq mathbf{coNP/poly}). We find examples of compositional problems, whose reoptimization versions do not have polynomial kernels under any of the considered local modifications. Finally, in another negative result, we prove that the reoptimization version of Connected Vertex Cover does not have a polynomial kernel unless Set Cover has a polynomial compression. In a different direction, looking at problems with polynomial kernels, we find that the reoptimization version of Vertex Cover has a polynomial kernel of size (varvec{2k+1}) using crown decompositions only, which improves the size of the kernel achievable with this technique in the classic problem.

In this paper, the regular languages of wire linear (hbox {AC}^0)are characterized as the languages expressible in the two-variable fragment of first-order logic with regular predicates, (mathrm{FO}^2[mathrm{reg}]). Additionally, they are characterized as the languages recognized by the algebraic class (mathbf {QLDA}). The class is shown to be decidable and examples of languages in and outside of it are presented.

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used. We compare our results with the ones obtained by the first author for exact synchronization, which is another version of synchronization studied in the literature, and draw some theoretical conclusions.

The well-known pumping lemma for regular languages states that, for any regular language L, there is a constant p (depending on L) such that the following holds: If (win L) and (vert wvert ge p), then there are words (xin V^{*}), (yin V^+), and (zin V^{*}) such that (w=xyz) and (xy^tzin L) for (tge 0). The minimal pumping constant ({{{,mathrm{mpc},}}(L)}) of L is the minimal number p for which the conditions of the pumping lemma are satisfied. We investigate the behaviour of ({{{,mathrm{mpc},}}}) with respect to operations, i. e., for an n-ary regularity preserving operation (circ ), we study the set ({g_{circ }^{{{,mathrm{mpc},}}}(k_1,k_2,ldots ,k_n)}) of all numbers k such that there are regular languages (L_1,L_2,ldots ,L_n) with ({{{,mathrm{mpc},}}(L_i)=k_i}) for (1le ile n) and ({{{,mathrm{mpc},}}(circ (L_1,L_2,ldots ,L_n)=~k}). With respect to Kleene closure, complement, reversal, prefix and suffix-closure, circular shift, union, intersection, set-subtraction, symmetric difference,and concatenation, we determine ({g_{circ }^{{{,mathrm{mpc},}}}(k_1,k_2,ldots ,k_n)}) completely. Furthermore, we give some results with respect to the minimal pumping length where, in addition, (vert xyvert le p) has to hold.

We consider the problem of weighted throughput in the single machine preemptive scheduling with continuous controllable processing times. A set of tasks can be scheduled on a single machine. Each task j is associated with a nonnegative weight (w_{j}), a release date, a due date, and an interval of possible processing times. A task j can either be scheduled with a total processing time (p_j) which is in the given interval, or rejected (not participating in the schedule). The reward for processing j for (p_{j}) time units is (w_{j}p_{j}), and we are interested in constructing a feasible preemptive schedule such that the sum of rewards is maximized. We present a dynamic programming algorithm that solves the problem in pseudo-polynomial time and use it to obtain an FPTAS. Afterward, as our main contribution we propose an interesting efficient frontier approach for improved complexity bounds.

This paper considers the structure consisting of the set of all words over a given alphabet together with the subword relation, regular predicates, and constants for every word. We are interested in the counting extension of first-order logic by threshold counting quantifiers. The main result shows that the two-variable fragment of this logic can be decided in twofold exponential alternating time with linearly many alternations (and therefore in particular in twofold exponential space as announced in the conference version (Kuske and Schwarz, in: MFCS’20, Leibniz International Proceedings in Informatics (LIPIcs) vol. 170, pp 56:1–56:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020) of this paper) provided the regular predicates are restricted to piecewise testable ones. This result improves prior insights by Karandikar and Schnoebelen by extending the logic and saving one exponent in the space bound. Its proof consists of two main parts: First, we provide a quantifier elimination procedure that results in a formula with constants of bounded length (this generalises the procedure by Karandikar and Schnoebelen for first-order logic). From this, it follows that quantification in formulas can be restricted to words of bounded length, i.e., the second part of the proof is an adaptation of the method by Ferrante and Rackoff to counting logic and deviates significantly from the path of reasoning by Karandikar and Schnoebelen.

This paper investigates presentations of lamplighter groups using computational models from automata theory. The present work shows that if G can be presented such that the full group operation is recognised by a transducer, then the same is true for the lamplighter group (G wr {{mathbb {Z}}}) of G. Furthermore, Cayley presentations, where only multiplications with constants are recognised by transducers, are used to study generalised lamplighter groups of the form (G wr {{mathbb {Z}}}^d) and (G wr F_d), where (F_d) is the free group over d generators. Additionally, ({{mathbb {Z}}}_k wr {{mathbb {Z}}}^2) and ({{mathbb {Z}}}_k wr {F_d}) are shown to be Cayley tree automatic.

We present an algorithm for constructing a depth-first search tree in planar digraphs; the algorithm can be implemented in the complexity class (text{ AC}^1(text{ UL }cap text{ co-UL})), which is contained in (text{ AC}^2). Prior to this (for more than a quarter-century), the fastest uniform deterministic parallel algorithm for this problem had a runtime of (O(log ^{10}n)) (corresponding to the complexity class (text{ AC}^{10}subseteq text{ NC}^{11})). We also consider the problem of computing depth-first search trees in other classes of graphs and obtain additional new upper bounds.

Secure and private computations over random access machine (RAM) are preferred over computations with circuits or Turing machines. Secure RAM executions become more and more important in the scope of avoiding information leakage when executing programs over a single computer, as well as the clouds. In this paper, we proposed a novel scheme for evaluating RAM programs without revealing any information on the computation, including the program, the data, and the result. We use Shamir Secret Sharing to share all the program instructions and the private string matching technique to ensure the execution of the right instruction sequence. We stress that our scheme obtains information-theoretical security and does not rely on any computational hardness assumptions.