Languages Accepted by Weighted Restarting Automata*

2021 ◽  
Vol 180 (1-2) ◽  
pp. 151-177
Author(s):  
Qichao Wang
Keyword(s):  
General Class ◽  
Formal Languages ◽  
Input Word ◽  
Additional Requirement ◽  
Tropical Semiring

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.

scholarly journals Scope-Bounded Pushdown Languages

2016 ◽  
Vol 27 (02) ◽  
pp. 215-233 ◽  
Author(s):  
Salvatore La Torre ◽  
Margherita Napoli ◽  
Gennaro Parlato
Keyword(s):  
Formal Language ◽  
Formal Languages ◽  
Formal Language Theory ◽  
Language Theory ◽  
Input Word ◽  
Model Of Computation ◽  
Bounded Number ◽  
Robust Model ◽  
Pushdown Automata

We study the formal language theory of multistack pushdown automata (MPA) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped MPA). We show that scoped MPA are indeed a robust model of computation, by focusing on the corresponding theory of visibly MPA (MVPA). We prove the equivalence of the deterministic and nondeterministic versions and show that scope-bounded computations of an n-stack MVPA can be simulated, rearranging the input word, by using only one stack. These results have some interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and the effective semilinearity of the Parikh image (Parikh's theorem). As a further contribution, we give a logical characterization and compare the expressiveness of the scope-bounded restriction with other MVPA classes from the literature. To the best of our knowledge, scoped MVPA languages form the largest class of formal languages accepted by MPA that enjoys all the above nice properties.

scholarly journals Máquina de Turing Analógica para Ensino de Linguagens Formais e Autômatos

2021 ◽  
Author(s):  
Leonardo Rebello Januário ◽  
Gustavo Henrique Müller ◽  
Alex Luciano Roesler Rese ◽  
Rudimar Luís Scaranto Dazzi ◽  
Thiago Felski Pereira
Keyword(s):  
Turing Machine ◽  
Formal Languages ◽  
Input Word ◽  
Input Tape ◽  
Computer Theory ◽  
Binary Alphabet

The article describes the development of a practical device for teachingin the area of Computer Theory. In the study, an adaptationof the Turing Machine is presented, using hardware and softwareintegration to interpret Formal Languages. Simulating an Automaton,sensors and motors are used to move the device head to the leftand right and to read and write the input tape. The developmentof the mechanism is described in two parts, the first includes thehardware that consists of the construction and adaptation of theTuring Machine, the second the implementation of the software andcommunication part between both. The developed device, allowsthe interpretation of a binary alphabet (0, 1), where an input word isaccepted, and as an output result, such device rejected or acceptedthe word.

A general class of processor interconnection strategies

1982 ◽  
Vol 10 (3) ◽  
pp. 90-98 ◽  
Author(s):  
Laxmi N. Bhuyan ◽  
Dharma P. Agrawal
Keyword(s):  
General Class

scholarly journals An Algebraic Brascamp–Lieb Inequality

2021 ◽  
Author(s):  
Jennifer Duncan
Keyword(s):  
General Class ◽  
Recent Progress ◽  
Algebraic Groups ◽  
Hölder’S Inequality ◽  
Duke Math ◽  
Rational Maps ◽  
Affine Invariant ◽  
Linear Maps ◽  
Nonlinear Maps ◽  
Funct Anal

AbstractThe Brascamp–Lieb inequalities are a very general class of classical multilinear inequalities, well-known examples of which being Hölder’s inequality, Young’s convolution inequality, and the Loomis–Whitney inequality. Conventionally, a Brascamp–Lieb inequality is defined as a multilinear Lebesgue bound on the product of the pullbacks of a collection of functions $$f_j\in L^{q_j}(\mathbb {R}^{n_j})$$ f j ∈ L q j ( R n j ) , for $$j=1,\ldots ,m$$ j = 1 , … , m , under some corresponding linear maps $$B_j$$ B j . This regime is now fairly well understood (Bennett et al. in Geom Funct Anal 17(5):1343–1415, 2008), and moving forward there has been interest in nonlinear generalisations, where $$B_j$$ B j is now taken to belong to some suitable class of nonlinear maps. While there has been great recent progress on the question of local nonlinear Brascamp–Lieb inequalities (Bennett et al. in Duke Math J 169(17):3291–3338, 2020), there has been relatively little regarding global results; this paper represents some progress along this line of enquiry. We prove a global nonlinear Brascamp–Lieb inequality for ‘quasialgebraic’ maps, a class that encompasses polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that both compensates for local degeneracies and yields a constant with minimal dependence on the underlying maps. We then show that this inequality generalises Young’s convolution inequality on algebraic groups with suboptimal constant.

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