Acta Informatica最新文献

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.

This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with timeout transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra with recursion, and a complete axiomatisation.

Programs are often subjected to significant optimizing and parallelizing transformations based on extensive dependence analysis. Formal validation of such transformations needs modelling paradigms which can capture both control and data dependences in the program vividly. Being value-based with an inherent scope of capturing parallelism, the untimed coloured Petri net (CPN) models, reported in the literature, fit the bill well; accordingly, they are likely to be more convenient as the intermediate representations (IRs) of both the source and the transformed codes for translation validation than strictly sequential variable-based IRs like sequential control flow graphs (CFGs). In this work, an efficient path-based equivalence checking method for CPN models of programs on integers is presented. Extensive experimentation has been carried out on several sequential and parallel examples. Complexity and correctness issues have been treated rigorously for the method.

Given a regular expression R and a string Q, the regular expression parsing problem is to determine if Q matches R and if so, determine how it matches, i.e., by a mapping of the characters of Q to the characters in R. Regular expression parsing makes finding matches of a regular expression even more useful by allowing us to directly extract subpatterns of the match, e.g., for extracting IP-addresses from internet traffic analysis or extracting subparts of genomes from genetic data bases. We present a new general techniques for efficiently converting a large class of algorithms that determine if a string Q matches regular expression R into algorithms that can construct a corresponding mapping. As a consequence, we obtain the first efficient linear space solutions for regular expression parsing.

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.