## Abstract state machines capture parallel algorithms (2003)

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Venue: | ACM Transactions on Computational Logic |

Citations: | 58 - 23 self |

### BibTeX

@ARTICLE{Blass03abstractstate,

author = {Andreas Blass and Yuri Gurevich},

title = {Abstract state machines capture parallel algorithms},

journal = {ACM Transactions on Computational Logic},

year = {2003},

volume = {4},

pages = {578--651}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets. \Lambda

### Citations

404 | Evolving Algebras 1993: Lipari Guide
- Gurevich
- 1995
(Show Context)
Citation Context .... . . . . . . 77 11.2 Unbounded Sequentiality and Submachines . . . . . . . . . . . 80 12 Actual or Potential Mailboxes 83 1s13 What Else Is There? 92 1 Introduction The Abstract State Machine Thesis =-=[9]-=- asserts that every algorithm is behaviorally equivalent to an abstract state machine and in particular is simulated step for step by that machine. There is considerable empirical evidence for this th... |

285 | Parallel Algorithms for Shared-Memory Machines - Karp, Ramachandran - 1990 |

114 | Sequential abstract state machines capture sequential algorithms
- Gurevich
(Show Context)
Citation Context ...every algorithm is behaviorally equivalent to an abstract state machine and in particular is simulated step for step by that machine. There is considerable empirical evidence for this thesis [15]. In =-=[11]-=-, the thesis was proved for sequential algorithms. The purpose of this paper is to extend the ideas and results of [11] to parallel algorithms. The algorithms we consider have computations divided log... |

65 | draft of the ASM guide - Gurevich - 1997 |

63 | Metafinite Model Theory - Grädel, Gurevich - 1998 |

31 | Ordinary interactive small-step algorithms, Part I - Blass, Gurevich - 2006 |

31 | and Vijaya Ramachandran, “Parallel algorithms for shared-memory machines - Karp - 1990 |

26 | Composition and submachine concepts for sequential ASMs
- Börger, Schmid
- 2000
(Show Context)
Citation Context ...tion of the submachine, though it may be many steps in its own right, counts as only a single step, like an intervention of the environment, for the larger machine. For details about submachines, see =-=[4, 12, 14]-=-. We can trivially modify the ASM in Figure 1 by delegating all its work to a submachine. Instead of using the counter phase to tell when the iteration should stop, let the submachine keep track of bo... |

18 | Sequential Abstract State Machines - Gurevich - 2000 |

16 | The logic of choice - Blass, Gurevich - 2000 |

15 | Partial Updates: Exploration
- Gurevich, Tillmann
(Show Context)
Citation Context ...lowing communication and interaction between processes, but not in a way that would introduce unbounded sequentiality. The framework developed here covers the partial updates described and studied in =-=[12, 14]-=- and used in the specification language AsmL [6]. Section 6 summarizes material on backgrounds from [3, 12], indicating its relevance to the matters discussed in the preceding sections. We assemble al... |

10 | Fixed point logics
- Dawar, Gurevich
(Show Context)
Citation Context ...corresponding to a fixed-point formula operates. For definiteness, we work with the inflationary fixed-point operator. (See the next paragraph, or for a general treatment of fixed-point operators see =-=[5]-=-.) Also, for brevity, we omit mention of free variables and values for them. The proclet p for IFPP;_x('(P; _x))(_t) seeks to compute the successive iterates \Phisn of the inflationary operator define... |

10 | Saharon Shelah, “Choiceless polynomial time,” Ann. Pure Appl. Logic 100 - Blass, Gurevich - 1999 |

6 | Margus Veanes, “Toward industrial strength abstract state machines,” Microsoft Research Technical Report MSR-TR-2001-98, available at http : //research.microsoft.com - Gurevich, Schulte |

5 | Vijaya "Parallel Algorithms for Shared Memory Machines - Karp, Ramachandran - 1990 |

5 | Processes are in the Eye of the Beholder
- Lamport
- 1994
(Show Context)
Citation Context ...although we regard algorithms as analyzable into proclets, we do not require that this analysis be unique. It is possible for an algorithm to be analyzable into subprocesses in more than one way; see =-=[17]-=- for an example. Even if such non-uniqueness were to persist down to the level of proclets, i.e., if an algorithm were decomposed into proclets in more than one way, then any of these ways would lead ... |

5 | Grädel and Antje Nowack, “Quantum Computing and Abstract State Machines - Erich |

4 | Interactive small-step algorithms I: Axiomatization, and II: Abstract state machines and the characterization theorem
- BLASS, GUREVICH, et al.
(Show Context)
Citation Context ...ent situation, it could require an extension of the notion of ASM. In fact, the study of intra-step interaction of an algorithm with its environment has led to an extension of the ASM framework; see [=-=Blass et al. 2006-=-]. But we do not know and couldn’t conceive a parallel algorithm that works in wide, shallow steps without intra-step interaction with its environment but does not fit the framework of our postulates.... |

3 | Background, reserve, and Gandy machines - Blass, Gurevich - 2000 |

3 | Quantum computing and abstract state machines - Gradel, Nowack - 2003 |

2 | Gurevich (2006): Ordinary Interactive Small-Step Algorithms, Part I - Blass, Yuri - 1145 |

2 |
Gurevich and Saharon Shelah, "Choiceless Polynomial Time", Microsoft Research
- Blass, Yuri
- 1999
(Show Context)
Citation Context ... abstract state machines. Part of the parallelism and thus part of the power of this model comes from allowing comprehension terms for multisets, analogous to the comprehension terms for sets used in =-=[2]-=-. In Section 10, we prove our main result, showing how the general parallel algorithms described in Section 7 can be simulated by abstract state machines. In particular, this shows that the partial up... |

2 | ASM guide,” Univ. of Michigan - Gurevich |

1 |
Neeraj Kayal, and Nitin Saxena, "PRIMES is in P," preprint (2002), available at http : ==www:cse:iitk:ac:in=news=primalityv 3:pdf
- Agrawal
(Show Context)
Citation Context ...here R is a polynomial-time computable binary relation, holding only between certain binary strings of equal length. Remark 12.2 (This remark was simplified on 1 August 2003 in light of the result of =-=[1]-=-.) As an indication of the possible complexity of find unique problems, we mention that this class of problems includes integer factorization. An instance of this problem is an integer (in binary nota... |

1 |
and Antje Nowack, "Quantum Computing and Abstract State Machines
- Gradel
(Show Context)
Citation Context ...n was algorithms where single steps can involve unbounded sequentiality, like the submachine algorithms in Section 11. We have also not mentioned quantum algorithms, but Gr"adel and Nowack have shown =-=[8]-=- that they can be modeled by ASMs (with an external function providing random bits); in fact, quantum states correspond to states in the sense of the present paper (so there are a great many of them i... |

1 |
Margus Veanes, "Toward industrial strength abstract state machines," Microsoft Research Technical Report MSR-TR-2001-98, available at http : ==research:microsoft:com
- Gurevich, Schulte
(Show Context)
Citation Context ... an update like S := T , a proclet may put an element into S with an update like S(a) := true or take an 14selement out of S. These situations are typical examples of the partial updates discussed in =-=[12]-=- and [14] and used in AsmL [6]. What is really happening in such situations is that the individual proclets are producing something other than updates to be included in the final \Delta (A; X). What t... |

1 | PRIMES is in P, To appear, available at http : //www.cse.iitk.ac.in/news/primality v3.pdf - AGRAWAL, KAYAL, et al. |

1 | Sequential-Time ASMs - GUREVICH, SCHULTE, et al. |

1 | Processes are in the eye of the beholder,” Theoret - Lamport - 1997 |