scholarly journals Weak Cost Register Automata are Still Powerful

2020 ◽  
Vol 31 (06) ◽  
pp. 689-709
Author(s):  
Shaull Almagor ◽  
Michaël Cadilhac ◽  
Filip Mazowiecki ◽  
Guillermo A. Pérez
Keyword(s):  
Weighted Automata ◽  
Tropical Semiring ◽  
Restricted Form ◽  
Counter Machines

We consider one of the weakest variants of cost register automata over a tropical semiring, namely copyless cost register automata over [Formula: see text] with updates using [Formula: see text] and increments. We show that this model can simulate, in some sense, the runs of counter machines with zero-tests. We deduce that a number of problems pertaining to that model are undecidable, namely equivalence, upperboundedness, and semilinearity. In particular, the undecidability of equivalence disproves a conjecture of Alur et al. from 2012. To emphasize how weak these machines are, we also show that they can be expressed as a restricted form of linearly-ambiguous weighted automata.

GENERIC ∊-REMOVAL AND INPUT ∊-NORMALIZATION ALGORITHMS FOR WEIGHTED TRANSDUCERS

2002 ◽  
Vol 13 (01) ◽  
pp. 129-143 ◽  
Author(s):  
MEHRYAR MOHRI
Keyword(s):  
Approximation Algorithm ◽  
Time Complexity ◽  
Full Description ◽  
Running Time ◽  
Weighted Automata ◽  
Tropical Semiring ◽  
Shortest Distance ◽  
Queue Discipline

We present a new generic ∊-removal algorithm for weighted automata and transducers defined over a semiring. The algorithm can be used with any semiring covered by our framework and works with any queue discipline adopted. It can be used in particular in the case of unweighted automata and transducers and weighted automata and transducers defined over the tropical semiring. It is based on a general shortest-distance algorithm that we briefly describe. We give a full description of the algorithm including its pseudocode and its running time complexity, discuss the more efficient case of acyclic automata, an on-the-fly implementation of the algorithm and an approximation algorithm in the case of the semirings not covered by our framework. We illustrate the use of the algorithm with several semirings. We also describe an input ∊-normalization algorithm for weighted transducers based on the general shortest-distance algorithm. The algorithm, which works with all semirings covered by our framework, admits an on-the-fly implementation.

Minimal Morality

2018 ◽  
Author(s):  
Michael Moehler
Keyword(s):  
Social Contract ◽  
Moral Pluralism ◽  
Moral Diversity ◽  
Moral Agents ◽  
Restricted Form ◽  
Pluralistic Societies ◽  
The Social ◽  
History Of ◽  
Just Society

This book develops a novel multilevel social contract theory that, in contrast to existing theories in the liberal tradition, does not merely assume a restricted form of reasonable moral pluralism, but is tailored to the conditions of deeply morally pluralistic societies that may be populated by liberal moral agents, nonliberal moral agents, and, according to the traditional understanding of morality, nonmoral agents alike. To develop this theory, the book draws on the history of the social contract tradition, especially the work of Hobbes, Hume, Kant, Rawls, and Gauthier, as well as on the work of some of the critics of this tradition, such as Sen and Gaus. The two-level contractarian theory holds that morality in its best contractarian version for the conditions of deeply morally pluralistic societies entails Humean, Hobbesian, and Kantian moral features. The theory defines the minimal behavioral restrictions that are necessary to ensure, compared to violent conflict resolution, mutually beneficial peaceful long-term cooperation in deeply morally pluralistic societies. The theory minimizes the problem of compliance by maximally respecting the interests of all members of society. Despite its ideal nature, the theory is, in principle, applicable to the real world and, for the conditions described, most promising for securing mutually beneficial peaceful long-term cooperation in a world in which a fully just society, due to moral diversity, is unattainable. If Rawls’ intention was to carry the traditional social contract argument to a higher level of abstraction, then the two-level contractarian theory brings it back down to earth.

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 Simple counter machines and number-theoretic problems

1979 ◽  
Vol 19 (2) ◽  
pp. 145-162 ◽  
Author(s):  
Eitan M. Gurari ◽  
Oscar H. Ibarra
Keyword(s):  
Counter Machines

scholarly journals Modeling of safe time Petri nets by interval weighted automata

2020 ◽  
Vol 53 (4) ◽  
pp. 187-192
Author(s):  
Jan Komenda ◽  
Aiwen Lai ◽  
José Godoy Soto ◽  
Sébastien Lahaye ◽  
Jean-louis Boimond
Keyword(s):  
Petri Nets ◽  
Time Petri Nets ◽  
Weighted Automata

scholarly journals Nested Weighted Automata

2017 ◽  
Vol 18 (4) ◽  
pp. 1-44 ◽  
Author(s):  
Krishnendu Chatterjee ◽  
Thomas A. Henzinger ◽  
Jan Otop
Keyword(s):  
Weighted Automata

scholarly journals PATH-EQUIVALENT DEVELOPMENTS IN ACYCLIC WEIGHTED AUTOMATA

2007 ◽  
Vol 18 (04) ◽  
pp. 799-811
Author(s):  
MATHIEU GIRAUD ◽  
PHILLIPE VEBER ◽  
DOMINIQUE LAVENIER
Keyword(s):  
Surface Area ◽  
Finite Automata ◽  
Clock Frequency ◽  
Partial Removal ◽  
Frequency Constraints ◽  
Weighted Automata ◽  
Weighted Finite Automata ◽  
Special Case

Weighted finite automata (WFA) are used with FPGA accelerating hardware to scan large genomic banks. Hardwiring such automata raises surface area and clock frequency constraints, requiring efficient ∊-transitions-removal techniques. In this paper, we present bounds on the number of new transitions for the development of acyclic WFA, which is a special case of the ∊-transitions-removal problem. We introduce a new problem, a partial removal of ∊-transitions while accepting short chains of ∊-transitions.

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