Ernst-Erich Doberkat
Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple parts, it is shown that factoring can be done in multiple steps, guided by these parts.
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We revisit here congruence relations for Büchi automata, which play a central role in the automata-based verification. The size of the classical congruence relation is in $3^{\mathcal{O}(n^2)}$, where $n$ is the number of states of a given Büchi automaton $\mathcal{A}$. Here we present improved congruence relations that can be exponentially coarser than the classical one. We further give asymptotically optimal congruence relations of size $2^{\mathcal{O}(n \log n)}$. Based on these optimal congruence relations, we obtain an optimal translation from Büchi automata to a family of deterministic f…
A Congruence-Based Perspective on Finite Tree Automata
本文利用树上的同余关系，研究树自动机的确定化与最小化，证明了一种Brzozowski风格的最小化算法，并扩展至词自动机情形。
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
Minimal History-Deterministic Co-Büchi Automata: Congruences and Passive Learning
本文提出基于同余的最小历史确定性共 Büchi 自动机的描述，并设计了一个多项式时间的被动学习算法，用于从标记示例中学习此类自动机。
Minimality of Random Moore Automata under Prefix-Dependent Congruences
研究随机确定性迁移系统中前缀依赖同余的平凡性，证明在标签独立且每个标签至少有三个可接受符号时，同余高概率为平凡。
On Minimization and Learning of Deterministic $ω$-Automata in the Presence of Don't Care Words
研究在存在不要关心词情况下确定性ω-自动机的最小化问题，证明了在任意不要关心词集合下确定性奇偶自动机优先级可高效最小化，并指出对于具有信息性右同余的确定性奇偶自动机，最小化问题为NP难。
Congruence-based Learning of Probabilistic Deterministic Finite Automata
本研究针对从语言模型学习概率确定性有限自动机的问题，提出扩展经典Myhill-Nerode同余的新同余以定义语言模型正则性，给出对应主动学习算法，还明确了语言模型可识别性与正则性的关系，为相关学习研究提供理论支撑。
Comparing Two Approaches to Include Stochasticity in Hybrid Automata
本文形式化并比较了分解调度与组合调度两种混合自动机随机扩展方法，分析其表达能力关系并对现有随机扩展进行分类。
Localising Stochasticity in Weighted Automata
该研究通过归一化将加权自动机转化为概率自动机，并揭示了加权自动机的行为可分解为指数增长和随机部分。
Stochastic automata over monoids as input sets are studied. The well-definedness of these automata requires an extension postulate that replaces the inherent universal property of free monoids. As a generalization of Turakainen's result, it will be shown that the generalized automata over monoids have the same acceptance power as their stochastic counterparts. The key to homomorphisms is a commuting property between the monoid homomorphism of input states and the monoid homomorphism of transition matrices. Closure properties of the languages accepted by stochastic automata over monoids are inv…
This work introduces a new problem, named as, affinity classification problem which is a generalization of the density classification problem. To solve this problem, we introduce temporally stochastic cellular automata where two rules are stochastically applied in each step on all cells of the automata. Our model is defined on 2-dimensional grid having affection capability. We show that this model can be used in several applications like modeling self-healing systems.
Logical and Algebraic Characterizations of Rational Transductions
本文将有界非周期语言的可判定性提升至有理转换，证明可判定给定同余类中的转换，并建立逻辑-代数等价传递，从而判定一阶可定义性，且该问题为PSPACE完全。
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular autom…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is not present in usual definitions. We show that this feature allows for strictly more behaviors (for instance, number conserving stochastic cellular automata require these local probabilistic correlations). We also show that several problems which are deceptively simple in the usual definitions, become undecidable when we allow for local probabilistic correl…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of solving the affinity classification problem. In addition to that, a cellular automaton, defined over Cayley tree, is shown as the classical searching problem solver. The proposed temporally stochastic cellular automata deals with two elementary cellular automata rules, say $f$ and $g$. The $f$ is the default rule, however, $g$ is temporally applied to the overall…
The theory of discrete stochastic systems has been initiated by the work of Shannon and von Neumann. While Shannon has considered memory-less communication channels and their generalization by introducing states, von Neumann has studied the synthesis of reliable systems from unreliable components. The fundamental work of Rabin and Scott about deterministic finite-state automata has led to two generalizations. First, the generalization of transition functions to conditional distributions studied by Carlyle and Starke. This in turn has led to a generalization of time-discrete Markov chains in wh…
Stochastic Hybrid Automata for Power Profile Modeling in Energy Systems
本文提出用随机混合自动机对能源系统功率曲线建模，形式化两种方法并给出构造规则，分析设计选择对复杂度的影响，并用工具验证可行性。
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the non-deterministic and stochastic settings. We then provide explicit tools to prove or disprove the existence of such a simulation between two stochastic cellular automata, even though the intrinsic simulation relation is shown to be undecidable in dimension two and higher. The key result behind this is the caracterizatio…
Stochastic finite automata arise naturally in many language and speech processing tasks. They include stochastic acceptors, which represent certain probability distributions over random strings. We consider the problem of efficient sampling: drawing random string variates from the probability distribution represented by stochastic automata and transformations of those. We show that path-sampling is effective and can be efficient if the epsilon-graph of a finite automaton is acyclic. We provide an algorithm that ensures this by conflating epsilon-cycles within strongly connected components. Sam…
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…
Stochastic Languages at Sub-stochastic Cost
本文针对加权自动机和成本寄存器自动机的随机性判定问题展开研究，证明一般CRA随机性不可判定，线性片段可通过谱方法多项式时间判定并具备局部亚随机特性，还给出了随机语言的代数刻画与随机正则表达式，为概率计算形式理论奠基。
Measuring Performance of Continuous-Time Stochastic Processes using Timed Automata
提出确定性时间自动机作为独立于模型的规范语言，用于定义连续时间随机过程的性能和可靠性度量，并针对半马尔可夫过程研究了这些度量的性质及近似算法。
Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their expressive power has thus far precluded them from effective analysis by probabilistic (and statistical) model checkers, stochastic game solvers, or analysis tools for Petri net-like formalisms. This paper presents the foundations and underlying algorithms for efficient MA modelling, reduction using static analysis, and most importantly, quantitative analysis…
Automata-Theoretic Verification of Interval Markov Decision Processes
本文研究区间马尔可夫决策过程的自动机理论验证，针对ω-正则规范，区分稳定与不稳定区间结构，分别使用适用于MDP和适用于博弈的自动机，并开发算法及概率保证，连接数据驱动建模与形式化验证。
Automata Learning -- Expect Delays!
本文针对带随机延迟的主动自动机学习提出将行为学习与延迟采样分离的方法，以减少根部过度采样，并在多个基准及数据库连接顺序场景中验证其优于朴素基线。
Good-for-MDP State Reduction for Stochastic LTL Planning
针对LTL目标下MDP随机规划中GFM自动机规模制约可扩展性的问题，提出GFM状态约简技术与GFφ类公式的单指数复杂度直接构造法，通过理论与实验验证了方法的有效性与可扩展性优势。
Learning Environment Models with Continuous Stochastic Dynamics
本文提出一种可扩展的自动机学习框架，通过降维和聚类处理连续动态环境，学习离散状态MDP模型，在多个OpenAI Gym基准上实现了高精度的控制策略，其性能可媲美甚至超越深度RL策略。
Minimum Reachability Probabilities in Rectangular Automata with Random Clocks
本文提出计算矩形自动机随机时钟下可达概率下界的方法，用于安全关键应用的最坏情况分析，并在电动汽车充电场景中验证了其可行性。
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