Related papers: Minimal Synthesis of String To String Functions Fr…
We consider the first problem that appears in any application of synchronizing automata, namely, the problem of deciding whether or not a given $n$-state $k$-letter automaton is synchronizing. First we generalize results from…
A minimal deterministic finite automaton (DFA) is uniformly minimal if it always remains minimal when the final state set is replaced by a non-empty proper subset of the state set. We prove that a permutation DFA is uniformly minimal if and…
In recent years, aligning a sequence to a pangenome has become a central problem in genomics and pangenomics. A fast and accurate solution to this problem can serve as a toolkit to many crucial tasks such as read-correction, Multiple…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…
The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language,…
We address the problem of building an index for a set $D$ of $n$ strings, where each string location is a subset of some finite integer alphabet of size $\sigma$, so that we can answer efficiently if a given simple query string (where each…
The Swap-Insert Correction distance from a string $S$ of length $n$ to another string $L$ of length $m\geq n$ on the alphabet $[1..d]$ is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting $S$ into $L$.…
This paper addresses the Data-Diff problem: given a dataset and a subsequent version of the dataset, find the shortest sequence of operations that transforms the dataset to the subsequent version, under a restricted family of operations. We…
The usage of Rational Speech Acts (RSA) framework has been successful in building \emph{pragmatic} program synthesizers that return programs which, in addition to being logically consistent with user-generated examples, account for the fact…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). We define two general strategies for generating synchronizing words, and we show that each of these strategies can be applied if and…
A word $w$ is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if $w$ sends all states of the automaton to a unique state. In 1964 Jan \v{C}erny found a sequence of n-state complete DFA…
In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…
The domains of data mining and knowledge discovery make use of large amounts of textual data, which need to be handled efficiently. Specific problems, like finding the maximum weight ordered common subset of a set of ordered sets or…
We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification.…
We give algorithms to accelerate the computation of deterministic finite automata (DFA) by calculating the state of a DFA n positions ahead utilizing a reverse scan of the next n characters. Often this requires scanning fewer than n…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work…
We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if…