Related papers: Gray Codes With Constant Delay and Constant Auxili…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
This paper introduces DeCAL, a new method for tokenwise compression. DeCAL uses an encoder-decoder language model pretrained with denoising to learn to produce high-quality, general-purpose compressed representations from the encoder. DeCAL…
Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination,…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
We study grammar-constrained decoding (GCD) as a coupling between an autoregressive next-token distribution and a reachability oracle over a pushdown system compiled from a context-free grammar (CFG). We prove an oracle invariance theorem:…
This paper presents a data stationary architecture in which each word has an attached address field. Address fields massively update in parallel to record data interchanges. Words do not move until memory is read for post processing. A sea…
We consider the problem of compressing memoryless binary data with or without side information at the decoder. We review the parity- and the syndrome-based approaches and discuss their theoretical limits, assuming that there exists a…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
Byte Pair Encoding (BPE) is a widely used tokenization algorithm, whose tokens cannot extend across pre-tokenization boundaries, functionally limiting it to representing at most full words. The BoundlessBPE and SuperBPE algorithms extend…
Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes…
Latent space based GAN methods and attention based sequence to sequence models have achieved impressive results in text generation and unsupervised machine translation respectively. Leveraging the two domains, we propose an adversarial…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…
We identify a hidden bottleneck in the information processing capacity of linear reservoir computers. When the measured features evolve linearly in the reservoir and the output is formed by linear readout with bias, we show that the…
In the online Steiner tree problem, a sequence of points is revealed one-by-one: when a point arrives, we only have time to add a single edge connecting this point to the previous ones, and we want to minimize the total length of edges…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…