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Introduction to the Theory of Computation

1996
*
ACM SIGACT News
*

algorithms
255

doi:10.1145/230514.571645
fatcat:wkcpm5qh5vavlf23rkn5axvxxu
*Complexity*relationships among models 258 7.2*The*Class P 260 Polynomial time 260 Examples*of**problems**in*P 262 7.3*The*Class NP 268 Examples*of**problems**in*NP 271*The*P versus ... 22 Exercises,*Problems*, and Solutions 25 Part*One*:*Automata*and Languages 29 1 Regular Languages 31 1.1 Finite*Automata*31 Formal definition*of*a finite automaton 35 Examples*of*finite*automata*...##
###
Page 4266 of Mathematical Reviews Vol. , Issue 83j
[page]

1983
*
Mathematical Reviews
*

*The*twelfth chapter

*of*

*the*book is an important

*one*,

*on*computational

*complexity*

*theory*. ...

*The*final chapters discuss new trends

*in*algebraic

*automata*

*theory*. ...

##
###
Undecidability of L(𝒜)=L(ℬ) recognized by measure many 1-way quantum automata
[article]

2021
*
arXiv
*
pre-print

We consider

arXiv:1308.3301v11
fatcat:ybm6yonqojftxhos6qopwnh2li
*the*languages equivalence*problem*, showing that * both strict and non-strict languages equivalence are*undecidable*; * to do this, we provide an additional proof*of**the**undecidability**of*non-strict ... and strict emptiness*of*MMQFA(EQFA), and then reducing*the*languages equivalence*problem*to emptiness*problem*; * Finally, some other Propositions derived from*the*above results are collected. ... Acknowledgements*The*author is very grateful to Dr. ...##
###
Preface for the special issue GandALF 2015

2018
*
Acta Informatica
*

*The*International Symposium

*on*Games,

*Automata*, Logics and Formal Verification (Gan-dALF) was founded

*in*2010 by a number

*of*Italian computer scientists interested

*in*mathematical logic,

*automata*

*theory*...

*The*programme consisted

*of*13 presentations

*on*algorithmic game

*theory*,

*automata*

*theory*, formal verification, and modal and temporal logics. ...

*The*International Symposium

*on*Games,

*Automata*, Logics and Formal Verification (Gan-dALF) was founded

*in*2010 by a number

*of*Italian computer scientists interested

*in*mathematical logic,

*automata*

*theory*...

##
###
Cellular automata as models of complexity

1984
*
Nature
*

Cellular

doi:10.1038/311419a0
fatcat:kbs6fi7g5vb6dhyuuzf6bdz6xq
*Automata*Cellular*automata*may serve as suitable models for a wide range*of*natural systems such as: •*The*growth*of*dendritic crystals (snowflakes) • Pigmentation patterns*on*mollusk shells This ... ,k-1) that update according to a deterministic rule depending*on*a neighborhood*Complex*behavior can arise from simple rules Introduction • Cellular*Automata*• Applications • Types*of*Cellular*Automata*... Computation*theory*• For class 3 and 4: •*the*occurrence*of*a particular length n site value sequence*in*infinite time is*undecidable*. • Decidable*in*finite time considering initial sequence length n0= ...##
###
What is known about the Value 1 Problem for Probabilistic Automata?
[article]

2014
*
arXiv
*
pre-print

Although

arXiv:1410.3770v1
fatcat:5golhfw4uvekrb6eg62ehxgtci
*undecidable*, this*problem*attracted a lot*of*attention over*the*last few years.*The*aim*of*this paper is to review and relate*the*results pertaining to*the*value 1*problem*. ...*The*value 1*problem*is a decision*problem*for probabilistic*automata*over finite words: are there words accepted by*the*automaton with arbitrarily high probability? ... We know that*the*Markov Monoid Algorithm cannot solve*the*value 1*problem*, as this*problem*is*undecidable*, but then what is*the**problem*solved by this algorithm? ...##
###
Page 7277 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

*The*main result

*in*this paper states that

*the*inclusion

*problem*is also

*undecidable*

*on*L =ab*c. A note added

*in*proof indicates that

*the*same holds for

*the*equivalence

*problem*. ... Summary: “

*In*this paper, some

*problems*that arise

*in*

*the*real- ization

*of*finite state machines (FSM) are shown to be strongly related to

*the*

*theory*

*of*submodular functions. ...

##
###
Computational classification of cellular automata

2012
*
International Journal of General Systems
*

We discuss attempts at

doi:10.1080/03081079.2012.695899
fatcat:sebvk4v4v5hblkb3gjwgcxu5ku
*the*classification*of*cellular*automata*,*in*particular with a view towards decidability. ... Even*in**the*decidable case, computational hardness poses a major obstacle for*the*automatic analysis*of*cellular*automata*. ... Hence we can construct cellular*automata*whose orbits are*undecidable*but complete knowledge*of**the*orbits*of**one**of**the*two*automata*will not help*in*deciding membership*in**the*orbits*of**the*other. ...##
###
Page 6192 of Mathematical Reviews Vol. , Issue 91K
[page]

1991
*
Mathematical Reviews
*

Summary: “

*The**problem**of*whether a given two- or higher-dimen- sional cellular automaton is reversible is shown to be algorithmi- cally*undecidable*. ... They extract*the*linear part*of*arbitrary rules, and provide an*in*- trinsic classification. Derivatives are applied to tracing*complexity*growth and*the*lattice gases. ...##
###
The Parameterized Complexity of Chosen Problems for Finite Automata on Trees
[chapter]

2011
*
Lecture Notes in Computer Science
*

There are many decision

doi:10.1007/978-3-642-21254-3_9
fatcat:of2rl2ihu5bvlowun3ho36w72q
*problems**in**automata**theory*(including membership, emptiness, emptiness*of*intersection, inclusion and universality*problems*) that for some classes*of*tree*automata*are NP-hard. ...*The*study*of*their parameterized*complexity*allows us to find new bounds*of*their non-polynomial time algorithmic behaviors. ...*In**the*classical*complexity**theory**the**complexity**of*a*problem*is measured by*the*amount*of*a resource (time or space) required to solve*the**problem*, which is presented as a function*of**the*size*of**the*...##
###
Preface

2007
*
Theoretical Computer Science
*

There is a dependency between computability

doi:10.1016/j.tcs.2007.04.018
fatcat:p7e6qof5pja4tceanzn44nwxam
*of*algorithmic*complexity*and decidability*of*different algorithmic Acknowledgements Finally, we warmly thank*the*referees for their reports and comments leading ... to better presentations*of**the*accepted papers, as well as to Giorgio Ausiello for important technical advice. ...*The*emphasis is*on*bounds*on**the**complexity**of*strings*in*constructively given subsets*of**the*Cantor space and comparison*of**the*Kolmogorov*complexity*to*the*subword*complexity**of*infinite strings. ...##
###
Decidability and Complexity Results for Timed Automata via Channel Machines
[chapter]

2005
*
Lecture Notes in Computer Science
*

*In*this paper we close this gap for timed

*automata*over infinite words by showing that

*the*

*one*-clock language inclusion

*problem*is

*undecidable*. ... However,

*the*status

*of*

*the*

*problem*when A has

*one*clock is not determined by [5] . ...

*The*density

*of*a timed word measures

*the*maximum number

*of*events

*in*any time unit along

*the*word. Theorem 5.

*The*universality

*problem*for

*one*-clock Büchi timed

*automata*is

*undecidable*. ...

##
###
Page 4134 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

*The*authors define alternating

*automata*working

*on*tree inputs as weaker variants

*of*similar

*automata*introduced

*in*a paper by 03 MATHEMATICAL LOGIC AND FOUNDATIONS 4134 Muller and Schupp [Theoret. ... This

*problem*is decidable for first-order languages but

*undecidable*for higher-order languages.

*In*fact, W. D. Goldfarb [Theoret. Com- put. ...

##
###
Page 4087 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

*The*paper is a general study

*on*

*the*fundamental issues

*of*pattern classification and learning

*theory*cast

*in*

*the*context

*of*classi- fication

*problems*. ... Paz [Introduction to probabilistic

*automata*, Academic Press, New York, 1971; MR 44 #6417], that

*the*emptiness

*problem*for probabilistic finite

*automata*(PFAs) is

*undecidable*. ...

##
###
Page 1164 of Mathematical Reviews Vol. , Issue 98B
[page]

1998
*
Mathematical Reviews
*

Summary: “

*The*first part*of*this paper surveys*the*use*of*finite models*in**automata**theory*. ...*The*second part*of*this paper is devoted to*the*use*of*finite models*in**the**complexity**theory**of*small-depth families*of*Boolean circuits. ...
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