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Added by
Trevor McDonell
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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No Arabic abstract
Haskell is a popular choice for hosting deeply embedded languages. A recurring challenge for these embeddings is how to seamlessly integrate user defined algebraic data types. In particular, one important, convenient, and expressive feature for creating and inspecting data -- pattern matching -- is not directly available on embedded terms. In this paper, we present a novel technique, embedded pattern matching, which enables a natural and user friendly embedding of user defined algebraic data types into the embedded language. Our technique enables users to pattern match on terms in the embedded language in much the same way they would in the host language.
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We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a practical compilation scheme from extended join definitions into ordinary ones plus ML pattern matching. To assess the correctness of our compilation scheme, we develop a theory of the applied join calculus, a calculus with value passing and value matching. We implement this calculus as an extension of the current JoCaml system.
We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing where application specific transformations are often applied to the input. By considering the class of polynomial transformations of the input, we provide fast algorithms and the first lower bounds for both new and old problems. Given a pattern of length m and a longer text of length n where both are assumed to contain integer values only, we first show O(n log m) time algorithms for pattern matching under linear transformations even when wildcard symbols can occur in the input. We then show how to extend the technique to polynomial transformations of arbitrary degree. Next we consider the problem of finding the minimum Hamming distance under polynomial transformation. We show that, for any epsilon>0, there cannot exist an O(n m^(1-epsilon)) time algorithm for additive and linear transformations conditional on the hardness of the classic 3SUM problem. Finally, we consider a version of the Hamming distance problem under additive transformations with a bound k on the maximum distance that need be reported. We give a deterministic O(nk log k) time solution which we then improve by careful use of randomisation to O(n sqrt(k log k) log n) time for sufficiently small k. Our randomised solution outputs the correct answer at every position with high probability.
Given an indeterminate string pattern $p$ and an indeterminate string text $t$, the problem of order-preserving pattern matching with character uncertainties ($mu$OPPM) is to find all substrings of $t$ that satisfy one of the possible orderings defined by $p$. When the text and pattern are determinate strings, we are in the presence of the well-studied exact order-preserving pattern matching (OPPM) problem with diverse applications on time series analysis. Despite its relevance, the exact OPPM problem suffers from two major drawbacks: 1) the inability to deal with indetermination in the text, thus preventing the analysis of noisy time series; and 2) the inability to deal with indetermination in the pattern, thus imposing the strict satisfaction of the orders among all pattern positions. This paper provides the first polynomial algorithm to answer the $mu$OPPM problem when indetermination is observed on the pattern or text. Given two strings with length $m$ and $O(r)$ uncertain characters per string position, we show that the $mu$OPPM problem can be solved in $O(mrlg r)$ time when one string is indeterminate and $rinmathbb{N}^+$. Mappings into satisfiability problems are provided when indetermination is observed on both the pattern and the text, and results concerning the general problem complexity are presented as well, with $mu$OPPM problem proved to be NP-hard in general.
We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$ minimization techniques to perform template detection in a multispectral image. We first adapt this minimization problem to work with compressive sensing data. Then we extend it to perform pattern detection using a formal transform called the spectralization along a pattern. That extension brings out the problem of measurement reconstruction. We introduce shifted measurements that allow us to reconstruct all the measurement with a small overhead and we give an optimality constraint for simple patterns. We present numerical results showing the performances of the original minimization problem and the compressed ones with different measurement rates and applied on remotely sensed data.
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