Related papers: Regular Languages in the Sliding Window Model
It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many…
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…
In this paper, we study arbitrary regular factorial languages over a finite alphabet $\Sigma$. For the set of words $L(n)$ of the length $n$ belonging to a regular factorial language $L$, we investigate the depth of decision trees solving…
We show how to utilize machine learning approaches to improve sliding window algorithms for approximate frequency estimation problems, under the ``algorithms with predictions'' framework. In this dynamic environment, previous…
We study regular expression membership testing: Given a regular expression of size $m$ and a string of size $n$, decide whether the string is in the language described by the regular expression. Its classic $O(nm)$ algorithm is one of the…
Streaming computation plays an important role in large-scale data analysis. The sliding window model is a model of streaming computation which also captures the recency of the data. In this model, data arrives one item at a time, but only…
We consider time-space tradeoffs for exactly computing frequency moments and order statistics over sliding windows. Given an input of length 2n-1, the task is to output the function of each window of length n, giving n outputs in total.…
Rule-based temporal query languages provide the expressive power and flexibility required to capture in a natural way complex analysis tasks over streaming data. Stream processing applications, however, typically require near real-time…
An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce…
We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this…
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…
The Random Language Model (De Giuli 2019) is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first language learning as a type of annealing in…
Large Language Models (LLMs) have shown exciting performance in listwise passage ranking. Due to the limited input length, existing methods often adopt the sliding window strategy. Such a strategy, though effective, is inefficient as it…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
The increasing popularity of jumbo frames means growing variance in the size of packets transmitted in modern networks. Consequently, network monitoring tools must maintain explicit traffic volume statistics rather than settle for packet…
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast…
In the sliding window model, we are required to maintain the target statistics over the most recent $n$ elements of a data stream, which is captured by a window of size $n$ sliding over the data stream. Exact computation usually requires…
While Large language models (LLMs) have proved able to address some complex reasoning tasks, we also know that they are highly sensitive to input variation, which can lead to different solution paths and final answers. Answer consistency…
Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…