Don't care words with an application totheautomata-based approach for real addition

Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of "don't cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdba

Longest repeated motif with a block of don't cares

International audienceWe introduce an algorithm for extracting all longest repeats with k don’t cares from a given sequence. Such repeats are composed of two parts separated by a block of k don’t care symbols. The algorithm uses suffix trees to fulfill this task and relies on the ability to answer the lowest common ancestor queries in constant time. It requires O(n log n) time in the worst-case

Advancing Dynamic Fault Tree Analysis

This paper presents a new state space generation approach for dynamic fault trees (DFTs) together with a technique to synthesise failures rates in DFTs. Our state space generation technique aggressively exploits the DFT structure --- detecting symmetries, spurious non-determinism, and don't cares. Benchmarks show a gain of more than two orders of magnitude in terms of state space generation and analysis time. Our approach supports DFTs with symbolic failure rates and is complemented by parameter synthesis. This enables determining the maximal tolerable failure rate of a system component while ensuring that the mean time of failure stays below a threshold

Efficient Enumeration of Non-Equivalent Squares in Partial Words with Few Holes

International audienceA partial word is a word with holes (also called don't cares: special symbols which match any symbol). A p-square is a partial word matching at least one standard square without holes (called a full square). Two p-squares are called equivalent if they match the same sets of full squares. Denote by psquares(T) the number of non-equivalent p-squares which are subwords of a partial word T. Let PSQUARES k (n) be the maximum value of psquares(T) over all partial words of length n with k holes. We show asympthotically tight bounds: c1 · min(nk 2 , n 2) ≤ PSQUARES k (n) ≤ c2 · min(nk 2 , n 2) for some constants c1, c2 > 0. We also present an algorithm that computes psquares(T) in O(nk 3) time for a partial word T of length n with k holes. In particular, our algorithm runs in linear time for k = O(1) and its time complexity near-matches the maximum number of non-equivalent p-squares

On Minimization and Learning of Deterministic ω\omega-Automata in the Presence of Don't Care Words

We study minimization problems for deterministic $\omega$-automata in the presence of don't care words. We prove that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don't care words. We derive that from a more general result from which one also obtains an efficient minimization algorithm for deterministic parity automata with informative right-congruence (without don't care words). We then analyze languages of don't care words with a trivial right-congruence. For such sets of don't care words it is known that weak deterministic B\"uchi automata (WDBA) have a unique minimal automaton that can be efficiently computed from a given WDBA (Eisinger, Klaedtke 2006). We give a congruence-based characterization of the corresponding minimal WDBA, and show that the don't care minimization results for WDBA do not extend to deterministic $\omega$-automata with informative right-congruence: for this class there is no unique minimal automaton for a given don't care set with trivial right congruence, and the minimization problem is NP-hard. Finally, we extend an active learning algorithm for WDBA (Maler, Pnueli 1995) to the setting with an additional set of don't care words with trivial right-congruence.Comment: Version 2 is a minor revision with a few references added, some additional explanations, and a few typos corrected Version 3: Added "On" to title, and added a reference for Corollary 4.

The credibility of monetary policy: a survey of the literature with some simple applications to Caanda

We don't have an abstract yet, sorry. But I think the title is pretty descriptive.monetary policy, credibility, dynamic inconsistency, inflation

Computing observability don't cares efficiently through polarization

A new method is presented to compute the exact observability don't cares (ODCs) for multiple-level combinational circuits. A new mathematical concept, called polarization, is introduced. Polarization captures the essence of ODC calculation on the otherwise difficult points of reconvergence. It makes it possible to derive the ODC of a node from the ODCs of its fanouts with a very simple formula. Experimental results for the 39 largest MCNC benchmark examples show that the method is able to compute the ODC set (expressed as a Boolean network) for all but one circuit in at most a few second

Public Perceptions of the Midwest’s Pavements - Iowa - Phase III

There are several objectives to this report. The first objective is to describe the sample with regard to the physical pavement data and three measures of driver satisfaction. In this section, the proportion of respondents who are satisfied with pavements on two-lane, rural, state highways will be examined and the distribution of pavement condition and roughness indices will be presented. The second objective will be a short description of the highway segments and any differences in satisfaction found between regions and pavement types. This was done in Phase II in each state and a letter sent showing the results in all three states. That letter sets forth the revised work plan and budget for Phase III of the project. The third objective is to describe the relationship between physical pavement characteristics and driver satisfaction. This will include a description of both the magnitude of relationship as well as identifying critical International Road Index (IRI) and Pavement Condition Index (PCI) cutoffs where a majority of the sample were satisfied. This will be done for comparative purposes with the Phase II approach, using the total sample to compute cumulative percentages responding to each of the three series of satisfaction questions