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Introduction to the Theory of Computation

Michael Sipser
1996 ACM SIGACT News  
algorithms 255 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  ... 
doi:10.1145/230514.571645 fatcat:wkcpm5qh5vavlf23rkn5axvxxu

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]

Tianrong Lin
2021 arXiv   pre-print
We consider 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.  ... 
arXiv:1308.3301v11 fatcat:ybm6yonqojftxhos6qopwnh2li

Preface for the special issue GandALF 2015

Javier Esparza, Enrico Tronci
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  ... 
doi:10.1007/s00236-018-0315-z fatcat:n26s76iwmzdxxclfuesecazq3m

Cellular automata as models of complexity

Stephen Wolfram
1984 Nature  
Cellular 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=  ... 
doi:10.1038/311419a0 fatcat:kbs6fi7g5vb6dhyuuzf6bdz6xq

What is known about the Value 1 Problem for Probabilistic Automata? [article]

Nathanaël Fijalkow
2014 arXiv   pre-print
Although 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?  ... 
arXiv:1410.3770v1 fatcat:5golhfw4uvekrb6eg62ehxgtci

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

Klaus Sutner
2012 International Journal of General Systems  
We discuss attempts at 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.  ... 
doi:10.1080/03081079.2012.695899 fatcat:sebvk4v4v5hblkb3gjwgcxu5ku

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]

Agata Barecka, Witold Charatonik
2011 Lecture Notes in Computer Science  
There are many decision 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  ... 
doi:10.1007/978-3-642-21254-3_9 fatcat:of2rl2ihu5bvlowun3ho36w72q


Mark Burgin, Cristian S. Calude
2007 Theoretical Computer Science  
There is a dependency between computability 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.  ... 
doi:10.1016/j.tcs.2007.04.018 fatcat:p7e6qof5pja4tceanzn44nwxam

Decidability and Complexity Results for Timed Automata via Channel Machines [chapter]

Parosh Aziz Abdulla, Johann Deneux, Joël Ouaknine, James Worrell
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.  ... 
doi:10.1007/11523468_88 fatcat:yaagqhcd6ncvbc7ri5gptos5uq

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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