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We consider online competitive algorithms for the problem of collecting weighted items from a dynamic queue S. The content of S varies over time. An update to S can occur between any two consecutive time steps, and it consists in deleting any number of items at the front of S and inserting other items into arbitrary locations in S. At each time step we are(More)
Let $\pi'_{w}$ denote the failure function of the Knuth-Morris-Pratt algorithm for a word w. In this paper we study the following problem: given an integer array $A'[1 \mathinner {\ldotp \ldotp }n]$ , is there a word w over an arbitrary alphabet Σ such that $A'[i]=\pi'_{w}[i]$ for all i? Moreover, what is the minimum cardinality of Σ required? We give an(More)
In this paper we consider word equations with one-variable (and arbitrarily many occurrences of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in general case the recompression is nondeterministic in case of one-variable it becomes deterministic and its running time(More)
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition, defined as S+T={m+n∣m∈S,n∈T}, and with ultimately periodic constants is exactly the class of hyper-arithmetical sets. Equations using addition only can represent(More)
In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and non-deterministic (NFAs), with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is employed: the SLPs are(More)
In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs(More)
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not(More)
In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs(More)
In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and non-deterministic (NFAs), with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are(More)
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