Paola Quaglia
We exploit the nondeterminism of LR parsing tables to reason about grammar ambiguity after a conflict-driven strategy. First, from parsing tables we define specialized structures, called SR-automata. Next, we search for ambiguous words along the paths of SR-automata that reach a conflict state and then diverge along the branches corresponding to distinct resolutions of the conflict.
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Nondeterministic tree-walking automata are not closed under complementation
该研究证明非确定性树游走自动机识别的树语言族不满足补封闭性，并进一步指出其表达能力强于无歧义树游走自动机，解决了相关开放问题。
This paper proves the decidability of the emptiness problem for two models which recognize graphs: graph-walking automata, and tilings of graphs by star subgraphs (star automata). Furthermore, it is proved that the non-emptiness problem for graph-walking automata (that is, whether a given automaton accepts at least one graph) is NEXP-complete. For star automata, which generalize nondeterministic tree automata to the case of graphs, it is proved that their non-emptiness problem is NP-complete.
Tree Automata and Tree Grammars
关于树语言理论，特别是可识别树语言和有限状态树变换的课堂讲稿。
Graph-walking automata (GWA) are a model for graph traversal using finite-state control: these automata move between the nodes of an input graph, following its edges. This paper investigates the effect of node-replacement graph homomorphisms on recognizability by these automata. It is not difficult to see that the family of graph languages recognized by GWA is closed under inverse homomorphisms. The main result of this paper is that, for $n$-state automata operating on graphs with $k$ labels of edge end-points, the inverse homomorphic images require GWA with $kn+O(1)$ states in the worst case.…
Subshifts defined by nondeterministic and alternating plane-walking automata
本文扩展Salo & Törma提出的平面行走自动机模型，引入非确定性和量词交替，证明其识别的子移位是sofics子移位的严格子类，存在/全称非确定性类不可比较且大于确定性类，还定义了交替量词层次结构并推测其严格性。
Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent One-Way and Two-Way Deterministic Automata
从概念复杂性的角度，研究了单向非确定有限自动机和上下文无关文法到Parikh等价的单向和双向确定有限自动机的转换.证明了对于每个具有$n$状态的单向非确定自动机，存在Parikh等价的分别具有$e^{O(\sqrt{n \ln n})}$和$p(n)$状态的单向和双向确定自动机，其中$p(n)$是多项式.此外，这些费用很紧张。相反，如果所有的话接受给定的自动机包含至少两个不同的字母，那么Parikh等价的单向确定性自动机的多项式数量的states.Concerning上下文无关文法，我们证明了，对于每个语法在乔姆斯基范式与h变量存在Parikh等价的单向和双向确定性自动机与$2^{O(h^2)}$和$2^{O(h)}$状态，分别。即使这些界限也很紧。
Deterministic Real-Time Tree-Walking-Storage Automata
本文研究确定性实时树行走存储自动机，证明其非擦除变体可接受2的幂和斐波那契长度等复杂一元语言，并确定其语言族位于正则与确定性上下文相关语言之间，同时分析了布尔与AFL闭包性质。
Plane-Walking Automata
在这篇文章中，我们研究了由多头有限自动机定义的多维子移位类，特别是定义为头数增长的子移位类的层次。该层次结构崩溃的第三个层次，所有的co-recursively可重复的子移位，在每个维度。我们还比较了这些类的SFT和sofic的变化。我们无法分离的第二和第三层次的一维和二维，并提出了一个相关的开放问题的两个计数器的机器。
Graph-walking automata (GWA) traverse graphs by moving between the nodes following the edges, using a finite-state control to decide where to go next. It is known that every GWA can be transformed to a GWA that halts on every input, to a GWA returning to the initial node in order to accept, and to a reversible GWA. This paper establishes lower bounds on the state blow-up of these transformations, as well as closely matching upper bounds. It is shown that making an $n$-state GWA traversing $k$-ary graphs halt on every input requires at most $2nk+1$ states and at least $2(n-1)(k-3)$ states in th…
Passive Model Learning of Visibly Deterministic Context-free Grammars
本文提出PAPNI算法，将RPNI推广到可见确定性下推自动机，在已知字母表分解的前提下实现确定性上下文无关文法的被动学习，并通过实验验证其预测准确率优于RPNI。
On the Generative Power of Omega-Grammars and Omega-Automata
ω-文法是用于生成ω-词（即无限长词）的形式文法，而ω-自动机是用于识别ω-词的自动机。本文给出了ω-文法和ω-自动机的干净而统一的定义，系统地研究了ω-文法相对于ω-自动机的生成能力，并给出了各种类型的ω-文法和接受模式的完整结果。我们使用元组（σ，ρ，π）来表示各种接受模式，其中σ表示某些指定的元素应该至少出现一次或无限次，ρ表示两个集合之间的某种二元关系，π表示正常或最左导子。在技术上，我们提出了（σ，ρ，π）-接受ω-文法，并系统地研究了它们相对于（σ，ρ）-接受ω-自动机的生成能力。我们给出了如何构造一些特殊形式的ω-文法，如ε-产生式自由ω-文法.通过建立转换技巧，研究了ω$-文法与ω-自动机之间的等价或包含关系.特别地，我们证明了对于某些接受模式，ω-CFG的生成能力严格弱于ω-PDA，而ω-CSG的生成能力等于ω-TM（而不是线性有界的ω-自动机类器件）.此外，我们提出了一些剩余的两个接受模式的开放问题。
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of "invisible" pebbles (as opposed to the usual "visible" ones). The resulting pebble tree automata recognize the regular tree languages (i.e., can validate all generalized DTD's) and hence can find all matches of MSO definable patterns. Moreover, when viewed as a navigational device, they lead to an XPath-like formalism that has a path expression for every MSO definable binary pattern. The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observabl…
A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by Sénizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for deterministic pushdown automata. The presented proof is conceptually simpler, and a particular novelty is that it is not given as two semidecision procedures but it provides an explicit algorithm that might be amenable to a complexity analysis.
Context-Free Grammars with Storage
上下文无关的S文法的介绍，为任意（存储）类型S，作为一个统一的框架，递归为基础的语法，自动机和传感器，视为程序。对于上下文无关的S文法的非终结符的每个出现，S类型的对象相关联，可以通过测试和操作对其进行操作，如文法规则中所指示的。以特定的存储类型给出特定的形式主义，如索引文法，自顶向下树转换器，属性文法等上下文无关的S文法等价于下推S自动机。本文引入语言的delta运算，从确定性单向S自动机语言得到上下文无关的S语言。
On the capabilities of grammars, automata, and transducers controlled by monoids
在过去的几十年里，语言理论中的经典模型已经被幺半群定义的控制机制所扩展。我们研究的么半群的原因扩展的上下文无关文法，有限自动机，或有限状态转换器，以超过原来的模型的能力。此外，我们调查时，在扩展的自动机模型中，不确定性的变体不同于确定性的能力。我们表明，所有这些条件实际上是等价的，并提出了一个代数特征。特别是，开放的问题，是否每一种语言所产生的价文法在有限幺半群是上下文无关的提供了一个肯定的答案。
Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis automata. This paper investigates the LL($k$) subclass of linear conjunctive grammars, defined by analogy with the classical LL($k$) grammars: these are grammars that admit top-down linear-time parsing with $k$-symbol lookahead. Two results are presented. First, every LL($k$) linear conjunctive grammar can be transformed to an LL(1) linear conjunctive grammar, and…
Parikh Image of Pushdown Automata
我们比较下推自动机（PDA的短）对其他表示。首先，我们表明，有一个家庭的PDA在一元字母表的$n$状态和$p \geq 2n + 4$堆栈符号，接受一个单一的长字，每一个等价的上下文无关文法需要$Ω(n^2(p-2n-4))$变量。这个家庭表明，经典的算法转换PDA到一个等效的上下文无关文法是最佳的，即使当字母表是一元。此外，我们观察到，语言等价和Parikh等价，它忽略了符号之间的顺序，这个家庭相吻合。我们的结论是，当假设这种较弱的等价性，转换算法也是最佳的。其次，Parikh定理激发了PDA与有限状态自动机的比较。特别是，同一个家庭的一元PDA给出了一个下界的状态数的每一个帕里克等价的有限状态自动机。最后，我们研究的情况下，一元确定性PDA。我们展示了一个新的建设转换成一个等价的上下文无关文法，达到最佳已知的界限一元确定性PDA。
On the Intersection Problem for Quantum Finite Automata
本文延续先前研究，探讨了 measure once 有限量子自动机模型，研究判定其识别的语言与有限指数或矩阵上下文无关文法生成的语言是否有非空交集的递归可判定性条件。
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these notes in a course. There are 61 exercises. I emphasize that automata are elementary playgrounds where we can explore the issues of deterministic and nondeterministic computation. Unlike P vs. NP, we can prove that nondeterminism is equivalent to determinism, or strictly more powerful than determinism, in finite-state and push-down automata respectively. I als…
Pushdown Automata and Context-Free Grammars in Bisimulation Semantics
本文在反应式图灵机及互模拟语义下，通过引入带中间接受的序列算子与状态感知概念，恢复了下推自动机与上下文无关文法之间的经典对应关系。
Techniques for Showing the Decidability of the Boundedness Problem of Language Acceptors
本文针对多数自动机/文法模型有界性问题可判定性未知的背景，提出多带自动机刻画、存储语言两种新技术，归约证明更大类单向非确定自动机和文法模型的有界性可判定。
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove that commutative images of languages of one-register automata are not always semi-linear, but they are always rational. We also lift the latter result to grammars: commutative images of one-register context-free languages are rational, and in consequence commutatively equivalent to register automata. We conjecture analogous results for automata and grammars w…
Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by Sénizergues (1998, 2005). We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order grammars. This ACKERMANN upper bound is optimal, and we also show that strong bisimilarity is primitive-recursive when the number of states of the automata is fixed.
We present an algorithm for extracting a subclass of the context free grammars (CFGs) from a trained recurrent neural network (RNN). We develop a new framework, pattern rule sets (PRSs), which describe sequences of deterministic finite automata (DFAs) that approximate a non-regular language. We present an algorithm for recovering the PRS behind a sequence of such automata, and apply it to the sequences of automata extracted from trained RNNs using the L* algorithm. We then show how the PRS may converted into a CFG, enabling a familiar and useful presentation of the learned language. Extracting…
Representing a P-complete problem by small trellis automata
电路值问题的被称为顺序NOR电路值问题的受限情况最近被用于获得表示P-完全语言的合取语法、布尔语法和语言方程的非常简洁的示例（Okhotin，http://dx.doi.org/10.1007/978-3-540-74593-8_23“A simple P-complete problem and its representations by language equations”，MCU 2007）。本文对这一问题提出了一种新的编码方法，并构造了一个具有11个状态的格状自动机（单向实时元胞自动机）来解决这一问题。
Precedence Automata and Languages
操作符先后次序语法定义了一个经典的布尔和确定性上下文无关族（称为Floyd语言或FL）。FL已经被证明严格包括众所周知的可见下推语言，并享受同样好的闭包属性。我们在这里介绍弗洛伊德自动机，一个等价的操作形式主义定义FL。这也允许扩展类来处理无限字符串，以执行例如模型检验。
Thinking outside the box is useless NFA = FNFA
本文针对任意维度图像的非确定性图像行走自动机，证明了允许跳出图像的自动机（NFA）与不允许的自动机（FNFA）能力等价，解决了长期存在的开放性问题。
Functional Automata - Formal Languages for Computer Science Students
介绍性形式语言课程暴露了先进的本科生和早期研究生的自动机理论，语法，建设性的证明，可计算性和可判定性。编程专业的学生发现这些主题很有挑战性，或者在许多情况下，是压倒性的，并且处于计算机科学的边缘。这种看法的存在并不完全荒谬，因为学生被要求设计和证明正确的机器和语法，而不能进行实验，也不能得到即时反馈，这在学习环境中是必不可少的。这篇文章提出了计算理论应该使用实际构建计算的工具来教授的论点。它描述了一个库，FSM，旨在为学生提供实验和测试他们的设计使用状态机，语法和正则表达式的机会，实现和课堂使用。学生能够在进行正式的正确性证明之前进行随机测试。也就是说，学生可以像在编程课程中一样测试他们的设计。此外，图书馆很容易让学生实现他们开发的算法，作为他们编写的建设性证明的一部分。为学生提供这种能力应该是形式语言课堂的新趋势。
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language classes. The function of the automata consists on recognizing words in a language generated by some grammar and expressed with letters from an alphabet. Such automata are, in principle, abstract entities and with suitable combinations of them we can represent any computation, no matter how complex. Their physical implementations are possible in any informati…
From Regexes to Parsing Expression Grammars
现在大多数脚本语言都使用regex模式匹配库。这些正则表达式库借用了正则表达式的语法，但具有不同于正则表达式语义的非正式语义，去除了交替的可交换性，并添加了无法通过形式主义表达的ad-hoc扩展，以有效识别正则语言，例如确定性有限自动机。解析表达式语法是一种形式化的语法，它可以描述所有确定性上下文无关语言，并且具有简单的计算模型。在本文中，我们提出了一个形式化的正则表达式通过转换到解析表达式文法。所提出的转换很容易容纳几个常见的正则表达式扩展，给它们一个正式的意义。它还提供了一个清晰的计算模型，有助于评估基于regex的匹配器的效率，并为它们指定可证明正确的优化提供了基础。
Cyclic Operator Precedence Grammars for Parallel Parsing
本文提出增强版的循环算符优先文法，取消相等优先关系的非循环假设，使其表达能力等同于其他OPL形式化方法，并能生成适合并行解析的无界平坦子结构。
Computational Model for Parsing Expression Grammars
本文为解析表达式文法（PEG）提出一种升级版确定性下推自动机计算模型，证明解析表达式语言包含 DCFLs 正则闭包的布尔闭包并对左拼接封闭，同时给出 2-way 版本的线性时间模拟算法。
Separating Parsing Expression Grammars using Cell-Probe Lower Bounds
该研究解决了PEG的三个公开问题，通过构造特定语言实例，证明PEG不满足反转、连接、Kleene星等多种封闭性，并利用单元探测下界技术在Lean 4中形式化了相关结论。
Parsing is a fundamental building block in modern compilers, and for industrial programming languages, it is a surprisingly involved task. There are known approaches to generate parsers automatically, but the prevailing consensus is that automatic parser generation is not practical for real programming languages: LR/LALR parsers are considered to be far too restrictive in the grammars they support, and LR parsers are often considered too inefficient in practice. As a result, virtually all modern languages use recursive-descent parsers written by hand, a lengthy and error-prone process that dra…
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