Ranked enumeration of MSO logic on words
Pierre Bourhis, Alejandro Grez, Louis Jachiet, Cristian Riveros

TL;DR
This paper introduces a framework for ranked enumeration of MSO logic solutions on words, enabling efficient, ordered output based on solution costs, with broad applicability to data queries and processing tasks.
Contribution
It presents a novel algorithm for enumerating MSO solutions on words in increasing order of cost with linear preprocessing and logarithmic delay, extending functional data structures.
Findings
Efficient enumeration with linear preprocessing and logarithmic delay.
Framework generalizes document spanners and complex event processing.
Algorithm uses extended functional Brodal queues for ranking.
Abstract
In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query one by one and without repetitions. This enumeration scheme is typically useful when the solutions are treated on the fly or when we want to stop the enumeration once the pertinent solutions have been found. However, with the current schemes, there is no restriction on the order how the solutions are given and this order usually depends on the techniques used and not on the relevance for the user. In this paper we study the enumeration of monadic second order logic (MSO) over words when the solutions are ranked. We present a framework based on MSO cost functions that allows to express MSO formulae on words with a cost associated with each solution.…
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