Filters








1,144 Hits in 1.7 sec

On permutation-reset automata

Elmar Dilger
1976 Information and Control  
A series decomposition of permutation-reset automata is set up.  ...  It is shown that a realization of this decomposition contains fewer components than in the usual Krohn-Rhodes decomposition of permutation-reset automata.  ...  PERMUTATION--REsET AUTOMATA We extend our results to permutation-reset automata.  ... 
doi:10.1016/s0019-9958(76)90466-6 fatcat:uzznllh4djgejpuu3adfcfaji4

Yet another proof of the cascade decomposition theorem for finite automata: Correction

Paul Zeiger
1968 Mathematical Systems Theory  
to a cascade of permutation-reset automata, Method IIA finishes the job.  ...  is permutation-reset, and hence no simpler than the original automaton.  ...  to a cascade of permutation-reset automata, Method IIA finishes the job.  ... 
doi:10.1007/bf01703267 fatcat:7swaj6y44baljnwjja5spnrclm

On Randomized Generation of Slowly Synchronizing Automata

Costanza Catalano, Raphaël M. Jungers, Michael Wagner
2018 International Symposium on Mathematical Foundations of Computer Science  
We report numerical results showing that our algorithm finds automata with much larger reset threshold than a mere uniform random generation and we present new families of automata with reset threshold  ...  Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n − 1.  ...  1 Table on upper bounds on the reset threshold for some classes of automata and examples of automata with large reset threshold belonging to these classes, up to date.  ... 
doi:10.4230/lipics.mfcs.2018.48 dblp:conf/mfcs/CatalanoJ18 fatcat:du76kamufvfyzdlrfh7ncogrcu

A new lower bound for reset threshold of synchronizing automata with sink state [article]

Dmitry Ananichev
2017 arXiv   pre-print
This improves on the previously known lower bound for the maximum reset threshold of binary synchronizing n-state automata with sink state.  ...  We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the n-state automaton in this series is n^2/4+2n-9.  ...  as permutation on Q n \ {1}.  ... 
arXiv:1701.07954v1 fatcat:re6tkjx32vanveldy22yj4nst4

On the Krohn-Rhodes Cascaded Decomposition Theorem [chapter]

Oded Maler
2010 Lecture Notes in Computer Science  
The Krohn-Rhodes theorem states that any deterministic automaton is a homomorphic image of a cascade of very simple automata which realize either resets or permutations.  ...  Moreover, if the automaton is counter-free, only reset automata are needed. In this paper we give a very constructive proof of a variant of this theorem due to Eilenberg.  ...  Definition 12 (Permutation-Reset Automata).  ... 
doi:10.1007/978-3-642-13754-9_12 fatcat:ei4c25zbcnhmveg4liv7wdn5ye

Invariance for ordinary differential equations: Correction

James A. Yorke
1968 Mathematical Systems Theory  
to a cascade of permutation-reset automata, Method IIA finishes the job.  ...  is permutation-reset, and hence no simpler than the original automaton.  ...  to a cascade of permutation-reset automata, Method IIA finishes the job.  ... 
doi:10.1007/bf01703268 fatcat:2dou3bbcfvbdxeho7x3vqpmwsu

On randomized generation of slowly synchronizing automata [article]

Costanza Catalano, Raphaël M. Jungers
2018 arXiv   pre-print
We report numerical results showing that our algorithm finds automata with much larger reset threshold than a mere uniform random generation and we present new families of automata with reset threshold  ...  Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n-1 .  ...  Acknowledgments The authors thank François Gonze and Vladimir Gusev for significant suggestions and fruitful discussions on the topic.  ... 
arXiv:1805.06723v2 fatcat:fwphmfcpibhwhbynwlr5jzgryq

Permutive One-Way Cellular Automata and the Finiteness Problem for Automaton Groups [chapter]

Martin Delacourt, Nicolas Ollinger
2017 Lecture Notes in Computer Science  
We provide a rst undecidability result on the dynamics of one-way permutive cellular automata, arguing in favor of the undecidability of the niteness problem for reset Mealy automata.  ...  The decidability of the niteness problem for automaton groups is a well-studied open question on Mealy automata.  ...  Fig. 1 . 1 linking reset Mealy automata to permutive OCA Proposition 1.  ... 
doi:10.1007/978-3-319-58741-7_23 fatcat:nu7u7bhvh5f5hbwnt26j5ar5pe

Generic Properties in Some Classes of Automaton Groups [chapter]

Thibault Godin
2019 Lecture Notes in Computer Science  
We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order.  ...  An unfolded reset automaton is minimal ([2] ) if and only if each states induces a different permutation on letters.  ...  Another, somewhat opposite, restriction on the transition function leads to the class of reset automata, studied e.g. in [22, 7] .  ... 
doi:10.1007/978-3-030-20981-0_7 fatcat:rjj3bpybb5gelouu2hgkc76s4q

Generic properties in some classes of automaton groups [article]

Thibault Godin
2019 arXiv   pre-print
We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order.  ...  An unfolded reset automaton is minimal ([2] ) if and only if each states induces a different permutation on letters.  ...  Another, somewhat opposite, restriction on the transition function leads to the class of reset automata, studied e.g. in [22, 7] .  ... 
arXiv:1903.11315v1 fatcat:w2jlblc5dbd6lgcfd6dx2hinze

Page 2349 of Mathematical Reviews Vol. 52, Issue 6 [page]

1976 Mathematical Reviews  
The main result of the paper says that a permutation-reset automaton that is connected under the permutation inputs and possesses a certain partition is isomorphic to a serial connection of two permutation-reset  ...  automata M,, M, that are connected under their permutation inputs.  ... 

On the effects of noise and speed on computations

Bernard Delyon, Oded Maler
1994 Theoretical Computer Science  
We prove upper and lower bounds on the effect of noise for various classes of finite automata.  ...  Maler, On the effects of noise and speed on computations, Theoretical Computer Science 129 (1994) 2799291.  ...  Nonrobustness of reset-free automata After establishing an upper bound on the distance for synchronizing automata, we would like to set a lower bound for the complementary class of reset-free automata.  ... 
doi:10.1016/0304-3975(94)90029-9 fatcat:gotyzkpudre2tllsekcvgrqlrq

On Direct Product and Quotient of Strongly Connected Automata [article]

Zino H. Hu
2013 arXiv   pre-print
An automaton is isomorphic to the direct product of a permutation strongly connected automaton and a synchronizing strongly connected automaton if and only if all of the following conditions are met: (  ...  strongly connected; (ii) the minimal ideal of its transition semigroup is a right group and (iii) the ranges of the idempotent elements of the minimal ideal of its transition semigroup form a partition on  ...  We have shown that we can decompose a quasi-ideal automaton into two strongly connected quotient automata, one is permuting and the other is synchronizing.  ... 
arXiv:1104.3314v10 fatcat:qr5nnv65cfcgjb4hmelgezroaa

Remarks on algebraic decomposition of automata

A. R. Meyer, C. Thompson
1969 Mathematical Systems Theory  
A version of the Krohn-Rhodes decomposition theorem for finite automata is proved in which capabilities as well as semigroups are preserved.  ...  INTRODUCTION The constructive half of Krohn and Rhodes 1 decomposition theorem for finite automata states that any finite automaton can be simulated by a. cascade of reset and permutation automata.  ...  A A is a permutation semiautomaton iff every cr € 2 is a permutation of A A Q # A is a reset iff every a € 2 . is a constant or identity function on Q ; constant functions are also called resets.  ... 
doi:10.1007/bf01746516 fatcat:4exq3zxarvdsxmhwq3eikmyna4

An Extremal Series of Eulerian Synchronizing Automata [chapter]

Marek Szykuła, Vojtěch Vorel
2016 Lecture Notes in Computer Science  
This improves the current lower bound on the length of shortest reset words in Eulerian automata.  ...  We present an infinite series of n-state Eulerian automata whose reset words have length at least (n^2-3)/2.  ...  For n ≥ 3, (n 2 − 3)/2 is an upper bound for the reset threshold of an n-state Eulerian synchronizing automaton. If |Σ| = 2, then the bound can be improved to (n 2 − 5)/2.  ... 
doi:10.1007/978-3-662-53132-7_31 fatcat:ex4hjccwo5bf5mtootc5odlbhm
« Previous Showing results 1 — 15 out of 1,144 results