A Congruence-Based Perspective on Finite Tree Automata

We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.

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A minimization algorithm for fuzzy top-down tree automata over lattices

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201298 ◽

2020 ◽

pp. 1-10

Author(s):

M. Ghorani ◽

S. Garhwal

Keyword(s):

Minimization Problem ◽

Time Complexity ◽

Tree Automaton ◽

Tree Automata ◽

Minimization Algorithm ◽

Top Down ◽

Minimal Form ◽

Minimization Algorithms ◽

The Given

In this paper, we study fuzzy top-down tree automata over lattices ( LTA s , for short). The purpose of this contribution is to investigate the minimization problem for LTA s . We first define the concept of statewise equivalence between two LTA s . Thereafter, we show the existence of the statewise minimal form for an LTA . To this end, we find a statewise irreducible LTA which is equivalent to a given LTA . Then, we provide an algorithm to find the statewise minimal LTA and by a theorem, we show that the output statewise minimal LTA is statewise equivalent to the given input. Moreover, we compute the time complexity of the given algorithm. The proposed algorithm can be applied to any given LTA and, unlike some minimization algorithms given in the literature, the input doesn’t need to be a complete, deterministic, or reduced lattice-valued tree automaton. Finally, we provide some examples to show the efficiency of the presented algorithm.

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A Physics-Based Formal Vocabulary of Energy Verbs for Function Modeling

Volume 1: 39th Computers and Information in Engineering Conference ◽

10.1115/detc2019-98502 ◽

2019 ◽

Author(s):

Chiradeep Sen ◽

Joshua D. Summers ◽

Xiaoyang Mao

Keyword(s):

Complex Systems ◽

Object Oriented ◽

Expressive Power ◽

Top Down ◽

Minimal Set ◽

Bottom Up ◽

Complex Engineered Systems ◽

Survey Results ◽

Engineered Systems

Abstract Function modeling of complex systems relies on predefined vocabularies of functions and flows. These vocabularies are usually developed in a top-down approach, i.e., by starting with a survey of existing systems and identifying their functions empirically. These vocabularies, while highly useful in manual modeling due to their expressive power and coverage, can be unsuitable for computerized modeling and reasoning, esp. for physics-based reasoning. To this end, this paper presents a physics-based vocabulary of function verbs developed using the bottom-up approach, where the need for the verbs is identified through a survey of physics phenomena involving operations on various energy forms allowed in physics. This survey results in a minimal set of only six verbs and two logical nodes that are proposed here. Each term is formally defined as object-oriented classes derived from more foundational classes proposed in prior research. The paper shows many applications of these terms, for modeling both simpler devices and more complex engineered systems. Collectively, this new vocabulary provides sufficient coverage over modeling needs and ensures models that are logically consistent and physics-wise valid.

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The Power of Weighted Regularity-Preserving Multi Bottom-Up Tree Transducers

International Journal of Foundations of Computer Science ◽

10.1142/s0129054115400109 ◽

2015 ◽

Vol 26 (07) ◽

pp. 987-1005 ◽

Cited By ~ 4

Author(s):

Andreas Maletti

Keyword(s):

Machine Translation ◽

Statistical Machine Translation ◽

Expressive Power ◽

Proof Technique ◽

Top Down ◽

Bottom Up ◽

Tree Transducer ◽

Negative Side ◽

Look Ahead ◽

Tree Transducers

The expressive power of regularity-preserving [Formula: see text]-free weighted linear multi bottom-up tree transducers is investigated. These models have very attractive theoretical and algorithmic properties, but (especially in the weighted setting) their expressive power is not well understood. Despite the regularity-preserving restriction, their power still exceeds that of composition chains of [Formula: see text]-free weighted linear extended top-down tree transducers with regular look-ahead. The latter devices are a natural super-class of weighted synchronous tree substitution grammars, which are commonly used in syntax-based statistical machine translation. In particular, the linguistically motivated discontinuous transformation of topicalization can be modeled by such multi bottom-up tree transducers, whereas the mentioned composition chains cannot implement it. On the negative side, the inverse of topicalization cannot be implemented by any such multi bottom-up tree transducer, which confirms their bottom-up nature (and non-closure under inverses). An interesting, promising, and widely applicable proof technique is used to prove these statements.

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Bottom-Up Parser: Look-Ahead LR Parser

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.c4666.098319 ◽

2019 ◽

Vol 8 (3) ◽

pp. 2406-2410

Keyword(s):

Second Step ◽

Minimization Algorithm ◽

Machine Code ◽

Top Down ◽

State Problem ◽

Bottom Up ◽

Look Ahead ◽

High Level ◽

The Given ◽

Lexical Analyzer

Compiler is used for the purpose of converting high level code to machine code. For doing this procedure we have six steps. On these steps the syntax analyses is the second step of compiler. The lexical analyzer produce token in the output. The tokens are used as input to syntax analyzer. Syntax analyzer performs parsing operation. The parsing can be used for deriving the string from the given grammar called as derivation. It depend upon how derivation will be performed either top down or bottom up. The bottom up parsers LR (Left-to-right), SLR (simple LR) has some conflicts. To remove these conflicts we use LALR (Look ahead LR parser). The conflicts are available if the state contains minimum two or more productions. If there is one shift operation in state and other one is reduce operation it means that shift-reduce operation at the same time. Then this state is called as inadequate state. This Inadequate state problem is solved in LALR parser. Other problem with other parsers is that they have more states as compared to LALR parser. So cost will be high. But in LALR parser minimum states used and cost will automatically be reduced. LALR is also called as Minimization algorithm of CLR (Canonical LR parser).

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The Bottom-Up Position Tree Automaton and the Father Automaton

International Journal of Foundations of Computer Science ◽

10.1142/s0129054120420034 ◽

2020 ◽

pp. 1-18

Author(s):

Samira Attou ◽

Ludovic Mignot ◽

Djelloul Ziadi

Keyword(s):

Tree Automaton ◽

Tree Automata ◽

Top Down ◽

Bottom Up ◽

Regular Tree ◽

The One ◽

Tree Expression

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, something which cannot be done with classical top-down approaches.

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