Acta Informatica最新文献

We consider a generalization of the classical 100 prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the unconstrained 100 prisoner problem. After introducing the 3 main classes of strategies, we define a variety of ‘hybrid’ strategies and quantify their winning-efficiency. Whenever analytic results are not available, we make use of Monte Carlo simulations to estimate with high accuracy the winning probabilities. Based on the results obtained, we conjecture that all strategies, except for the strategy maximizing the winning probability of the classical (constrained) problem, converge to the random strategy under weak conditions on the number of players or empty boxes. We conclude by commenting on the possible applications of our results in understanding processes of information retrieval, such as “memory” in living organisms.

Message-based systems are usually distributed in nature, and distributed components collaborate via asynchronous message passing. In some cases, particular ordering among the messages may lead to violation of the desired properties such as data confidentiality. Due to the absence of a global clock and usage of off-the-shelf components, such unwanted orderings can be neither statically inspected nor verified by revising their codes at design time. We propose a choreography-based runtime verification algorithm that given an automata-based specification of unwanted message sequences detects the formation of the unwanted sequences. Our algorithm is fully decentralized in the sense that each component is equipped with a monitor, as opposed to having a centralized monitor, and also the specification of the unwanted sequences is decomposed among monitors. In this way, when a component sends a message, its monitor inspects if there is a possibility for the formation of unwanted message sequences. As there is no global clock in message-based systems, monitors cannot determine the exact ordering among messages. In such cases, they decide conservatively and declare a sequence formation even if that sequence has not been formed. We prevent such conservative declarations in our algorithm as much as possible and then characterize its operational guarantees. We evaluate the efficiency and scalability of our algorithm in terms of the communication overhead, the memory consumption, and the latency of the result declaration through simulation.

A temporal graph with lifetime L is a sequence of L graphs (G_1, ldots ,G_L), called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always connected if each layer is a connected graph, and it is k-edge-deficient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always-connected, k-edge-deficient temporal graphs with sufficient lifetime can always be explored in (O(kn log n)) time steps. We also construct always-connected, k-edge-deficient temporal graphs for which any exploration requires (varOmega (n log k)) time steps. For always-connected, 1-edge-deficient temporal graphs, we show that O(n) time steps suffice for temporal exploration.

Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property (varPhi ). What happens if this question is modified in a way that we get a possibly infinite family of graphs as an input, and the question is if there is a graph satisfying (varPhi ) in the family? We approach this question by using formal languages for specifying families of graphs, in particular by regular sets of words. We show that certain graph properties can be decided by studying the syntactic monoid of the specification language L if a certain torsion condition is satisfied. This condition holds trivially if L is regular. More specifically, we use a natural binary encoding of finite graphs over a binary alphabet (varSigma ), and we define a regular set (mathbb {G}subseteq varSigma ^*) such that every nonempty word (win mathbb {G}) defines a finite and nonempty graph. Also, graph properties can then be syntactically defined as languages over (varSigma ). Then, we ask whether the automaton (mathcal {A}) specifies some graph satisfying a certain property (varPhi ). Our structural results show that we can answer this question for all “typical” graph properties. In order to show our results, we split L into a finite union of subsets and every subset of this union defines in a natural way a single finite graph F where some edges and vertices are marked. The marked graph in turn defines an infinite graph (F^infty ) and therefore the family of finite subgraphs of (F^infty ) where F appears as an induced subgraph. This yields a geometric description of all graphs specified by L based on splitting L into finitely many pieces; then using the notion of graph retraction, we obtain an easily understandable description of the graphs in each piece.

The regular intersection emptiness problem for a decision problem P (({{textit{int}}_{{mathrm {Reg}}}})(P)) is to decide whether a potentially infinite regular set of encoded P-instances contains a positive one. Since ({{textit{int}}_{{mathrm {Reg}}}})(P) is decidable for some NP-complete problems and undecidable for others, its investigation provides insights in the nature of NP-complete problems. Moreover, the decidability of the ({{textit{int}}_{{mathrm {Reg}}}})-problem is usually achieved by exploiting the regularity of the set of instances; thus, it also establishes a connection to formal language and automata theory. We consider the ({{textit{int}}_{{mathrm {Reg}}}})-problem for the well-known NP-complete problem Integer Linear Programming (ILP). It is shown that any DFA that describes a set of ILP-instances (in a natural encoding) can be reduced to a finite core of instances that contains a positive one if and only if the original set of instances did. This result yields the decidability of ({{textit{int}}_{{mathrm {Reg}}}})(ILP).

It cannot be decided whether a pushdown automaton accepts using a pushdown height, which does not depend on the input length, i.e., when it accepts using constant height. Furthermore, when a pushdown automaton accepts in constant height, the height can be arbitrarily large with respect to the size of the description of the machine, namely it does not exist any recursive function in the size of the description of the machine bounding the height of the pushdown. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the situation is different. First, acceptance in constant height is decidable. Moreover, in the case of acceptance in constant height, the height is at most exponential with respect to the size of the description of the pushdown automaton. We also prove a matching lower bound. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal.

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.