Evgenija Bondar, Mikhail Volkov
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs and trees.
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely reachable automata in terms of certain directed graphs.
Completely Reachable Almost Group Automata
本文研究字母表由一个亏格为1的字母和一组置换组成的有限确定性自动机，刻画其完全可达的条件，重点分析置换生成传递非本原群的情形。
This article focuses on subset reachability in synchronizing automata. First, we provide families of synchronizing automata with subsets which cannot be reached with short words. These families do not fulfil Don's Conjecture about subset reachability. Moreover, they show that some subsets need exponentially long words to be reached, and that the restriction of the conjecture to included subsets also does not hold. Second, we analyze completely reachable automata and provide a counterexample to the conjecture of Bondar and Volkov about the so-called $Γ_1$-graph. We finally prove an alternative …
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a polynomial-time algorithm for recognizing this class of automata.
Don's conjecture for binary completely reachable automata: an approach and its limitations
本文针对完全可达自动机中 Don 猜想（每个 $k$ 状态集可由长度至多 $n(n-k)$ 的词实现）在二元字母且满足特定限制时给出证明，并讨论方法的局限性。
Completely reachable automata: a quadratic decision algorithm and a quadratic upper bound on the reaching threshold
针对完全可达自动机的判定复杂度问题，提出时间与空间复杂度分别为${\rm{\textit{O}(|Σ|\cdot n^2)}}$和$\textit{O}(|Σ|\cdot n)$的二次决策算法，并证明弱Don猜想，给出该类自动机最短同步单词长度的二次上界。
We study three notions of directability of fuzzy automata akin to the D1-, D2- and D3-directability of nondeterministic automata. Thus an input word $w$ of a fuzzy automaton is D1-directing if a fixed single state is reachable by $w$ from all states, D2-directing if exactly the same states are reachable by $w$ from every state, and D3-directing if there is a state reachable by $w$ from every state. We study the various sets of directing words of fuzzy automata, prove that the directability properties are decidable, and show how such results can be deduced from the theory of directable nondeter…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete reachability.Here, we take a closer look at generalized circular and completely reachable automata. We derive that over a binary alphabet every completely reachable automaton must be circular, a consequence of a structural result stating that completely reachable automata over strictly less letters than states always contain permutational letters. We state sufficien…
We give a new characterization of primitive permutation groups tied to the notion of completely reachable automata. Also, we introduce sync-maximal permutation groups tied to the state complexity of the set of synchronizing words of certain associated automata and show that they are contained between the $2$-homogeneous and the primitive groups. Lastly, we define $k$-reachable groups in analogy with synchronizing groups and motivated by our characterization of primitive permutation groups. But the results show that a $k$-reachable permutation group of degree $n$ with $6 \le k \le n - 6$ is eit…
Around Don's conjecture for binary completely reachable automata
本文研究完全可达 DFA 中可达字长度的 Don 猜想，构造反例并证明标准化 DFA 的长度上界，且在附加条件下证实该猜想。
Parametric updates in parametric timed automata
本文提出一类新的参数化时间自动机，允许时钟更新为参数值，并针对EF-空性问题，通过限制更新所有时钟的语法子类，实现了可判定性和精确综合。
Completely Reachable Road Coloring
研究哪些有向图能用有限字母表边标记成完全可达自动机，其识别在多项式时间内，标签字母表大小固定时成NP完全问题，还对特定有向图进行分类。
Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by terms, and sets of states by Tree Automata (TA). The central problem in TRMC is to decide whether a set of bad states is reachable. The problem of computing a TA representing (an over- approximation of) the set of reachable states is undecidable, but efficient solutions based on completion or iteration of tree transducers exist. Unfortunately, the TRMC framework is unable to efficiently capture both the complex structure of a system and of some of its…
We consider the problem of state-space reduction for nondeterministic weakly-hierarchical visibly pushdown automata (VPA). VPA recognize a robust and algorithmically tractable fragment of context-free languages that is natural for modeling programs. We define an equivalence relation that is sufficient for language-preserving quotienting of VPA. Our definition allows to merge states that have different behavior, as long as they show the same behavior for reachable equivalent stacks. We encode the existence of such a relation as a Boolean partial maximum satisfiability (PMax-SAT) problem and pre…
A Term-based Approach for Generating Finite Automata from Interaction Diagrams
本文提出一种从 UML Sequence Diagrams 等交互语言生成非确定性有限自动机（NFA）的新方法，通过操作语义和交互合并简化技术，在不依赖昂贵归约技术的前提下生成缩减的 NFA，并验证了其在 trace analysis 中的应用效果。
Under the assumption $\mathcal{P} \neq \mathcal{NP}$, we prove that two natural problems from the theory of synchronizing automata cannot be solved in polynomial time. The first problem is to decide whether a given reachable partial automaton is synchronizing. The second one is, given an $n$-state binary complete synchronizing automaton, to compute its reset threshold within performance ratio less than $d \ln{(n)}$ for a specific constant $d>0$.
Prime Accessible Deterministic Automata
本文对有限字母表上的素可达确定性自动机分类，补充了单字母表及多字母表下的素自动机判定条件，给出有限情形的简短证明，还刻画了状态为有限输入字的自动机的分解。
We show that if a semisimple synchronizing automaton with $n$ states has a minimal reachable non-unary subset of cardinality $r\ge 2$, then there is a reset word of length at most $(n-1)D(2,r,n)$, where $D(2,r,n)$ is the $2$-packing number for families of $r$-subsets of $[1,n]$.
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 \cite{RandSynch},\cite{On2Problems} for the case of strongly connected partial automata. Specifically, for $k>1$ we show that an automaton is synchronizing with probability $1-O(\frac{1}{n^{0.5k}})$ and present an algorithm with linear in $n$ expected time, while the best known algorithm is quadratic on each instance. This results are interesting due to their applications…
This paper deals with the CREP (Configuration REachability Problem) for non-uniform cellular automata (CAs). The cells of non-uniform CAs, we have considered here, can use different Wolfram's rules to generate their next states. We report an algorithm which decides whether or not a configuration of a given (non-uniform) cellular automaton is reachable from another configuration. A characterization tool, named Reachability tree, is used to develop theories and the decision algorithm for the CREP. Though the worst case complexity of the algorithm is exponential in time and space, but the average…
The languages of infinite timed words accepted by timed automata are traditionally defined using Buchi-like conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natural quantitative semantics for timed automata based on the so-called frequency, which measures the proportion of time spent in the accepting locations. We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems.
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of terms reachable by a rewriting relation. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approximation and influencing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on E and T(F) for c…
We propose two hard problems in cellular automata. In particular the problems are: [DDP$^M_{n,p}$] Given two \emph{randomly} chosen configurations $t$ and $s$ of a cellular automata of length $n$, find the number of transitions $τ$ between $s$ and $t$. [SDDP$^δ_{k,n}$] Given two \emph{randomly} chosen configurations $s$ of a cellular automata of length $n$ and $x$ of length $k<n$, find the configuration $t$ such that $k$ number of cells of $t$ is fixed to $x$ and $t$ is reachable from $s$ within $δ$ transitions. We show that the discrete logarithm problem over the finite field reduces to DDP$^…
A Complexity Dichotomy for Semilinear Target Sets in Automata with One Counter
该研究针对三类单计数器系统，通过引入Presburger公式的通用框架，证明了半线性目标集问题的复杂性二分定理，且可判定公式所属的复杂度侧。
The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational problems related to synchronization and to the length of synchronizing words. Hence, it is natural to investigate synchronizing automata extremal with this property, i.e., such that the minimal deterministic automaton for the set of synchronizing words has $2^n - n$ states. The sync-maximal permutation groups have been introduced in [{\sc S. Hoffmann}, Complete…
Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since its introduce, VPAs have been shown to be useful in various context, e.g., as specification formalism for verification and as automaton model for processing XML streams. Due to high complexity, however, implementation of formal verification based on VPA framework is a challenge. In this paper we consider the problem of implementing VPA-based model checking algor…
We cast new light on the existing models of one-way deterministic topological automata by introducing a fresh but general, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a configuration, continues to evolve in a topological space by applying continuous transition operators one by one. The acceptance and rejection of a given input are determined by observing the interior system after the input is completely processed. Such automata naturally generalize one-way finite automata of various types, including deterministic, probabilistic, quantu…
Herein we survey the main results concerning quantum automata and machines with classical control. These machines were originally proposed by Sernadas et al in [37], during the FCT QuantLog project. First, we focus on the expressivity of quantum automata with both quantum and classical states. We revise the result obtained in [32] where it was proved that such automata are able to recognise, with exponentially less states than deterministic finite automata, a family of regular languages that cannot be recognised by other types of quantum automata. Finally, we revise the concept of quantum Turi…
Optimal and Robust Controller Synthesis: using Energy Timed Automata with Uncertainty
本文提出了一种新的框架，用于综合鲁棒且最优的能量感知控制器，基于能量时序自动机，能够方便地表达时间约束和可变能量速率。证明了在确定性和不确定性能量速率设置中，能量约束无限运行问题的可决定性，并考虑了确定最小上界以允许能量约束无限运行的优化问题。
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or parallel algorithm if and only if it has a small locality. In this work we seek to automate the study of solvability and locality: given the description of a graph problem $Π$, we would like to determine if $Π$ is solvable and what is the asymptotic locality of $Π$ as a function of the size of the graph. Put otherwise, we seek to automatically synthesize ef…
Individual machines in flexible production lines explicitly expose capabilities at their interfaces by means of parametric skills. Given such a set of configurable machines, a line integrator is faced with the problem of finding and tuning parameters for each machine such that the overall production line implements given safety and temporal requirements in an optimized and robust fashion. We formalize this problem of configuring and orchestrating flexible production lines as a parameter synthesis problem for systems of parametric timed automata, where interactions are based on skills. Paramete…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。