## Expressiveness of $-Calculus: What Matters? (2000)

Venue: | Advances in Soft Computing, Proc. of the 9th Intern. Symp. on Intelligent Information Systems IIS'2000, Bystra |

Citations: | 7 - 6 self |

### BibTeX

@INPROCEEDINGS{Eberbach00expressivenessof,

author = {Eugene Eberbach},

title = {Expressiveness of $-Calculus: What Matters?},

booktitle = {Advances in Soft Computing, Proc. of the 9th Intern. Symp. on Intelligent Information Systems IIS'2000, Bystra},

year = {2000},

pages = {145--157},

publisher = {Physica-Verlag}

}

### OpenURL

### Abstract

$-calculus is a higher-order polyadic process algebra for resource bounded computation. It has been designed to handle autonomous agents, evolutionary computing, neural nets, expert systems, machine learning, and distributed interactive AI systems, in general. $-calculus has built-in cost-optimization mechanism allowing to deal with nondeterminism, incomplete and uncertain information. In this paper, we investigate expressiveness of $-calculus. We show that due to innitary means, it allows to express models having richer behavior than Turing machine, including cellular automata, interaction machines, neural networks, and random automata networks. We also investigate the importance of synchronization, representation of continuity, and higher-order.

### Citations

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Citation Context ...ogether with closely related decisiontheoretic metareasoning are two new promising techniques and their application to general decision-making architectures has not yet been investigated in any depth =-=[22]-=-. $-calculus attempts to formalize resource bounded computation using process algebras. To avoid combinatorial explosion, on-line optimization often considers a restricted subset of agents, and only a... |

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Citation Context ...urce bounded computation attempts to nd the best answer possible given operational constraints. The approach is known under a variety of names, including AEexible computation [14], anytime algorithms =-=[3]-=-, imprecise-computation [16], or design-to-time scheduling [11]. Anytime algorithms together with closely related decisiontheoretic metareasoning are two new promising techniques and their application... |

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Citation Context ...eneration, fault-tolerant systems, computer viruses, machine learning, and evolvable hardware. The work is related to other general models for sequential and parallel computation, including -calculus =-=[2]-=- and -calculus [1820]. The $-calculus leads to a new programming paradigm: cost languages, and a new class of computer architectures: cost-driven machines [4]. In this paper, we concentrate on the pro... |

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Citation Context ... of the higher-order features, we could also encode higher-order -calculus (HO) in $-calculus. We assume that in a function denition, a function name can be either a constant or a variable. Sangiorgi =-=[23,19]-=- has proved that higher-order -calculus is not more expressive than (rst-order) -calculus. Thus such simulation becomes superAEuous. From the above and Milner in [19] showed has to simulate -calculus ... |

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Citation Context ...tempts to nd the best answer possible given operational constraints. The approach is known under a variety of names, including AEexible computation [14], anytime algorithms [3], imprecise-computation =-=[16]-=-, or design-to-time scheduling [11]. Anytime algorithms together with closely related decisiontheoretic metareasoning are two new promising techniques and their application to general decision-making ... |

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Citation Context ... we can encode -calculus and -calculus. Next we will show that $-calculus can express formalisms which have richer behavior than Turing machines: including cellular automata [1], interaction machines =-=[24,25,27,28,13]-=-, neural networks, and automata networks [12], exactly due to allowing innite (but enumerable) application of the parallel composition operator. Example 31 Encoding of the -calculus Because $-calculus... |

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Citation Context ...bounded computation. Resource bounded computation attempts to nd the best answer possible given operational constraints. The approach is known under a variety of names, including AEexible computation =-=[14]-=-, anytime algorithms [3], imprecise-computation [16], or design-to-time scheduling [11]. Anytime algorithms together with closely related decisiontheoretic metareasoning are two new promising techniqu... |

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Citation Context ...mitted, thus asynchronous -calculus becomes a subset of isynchronousj -calculus. Then, for instance, the leader election problem can be solved in synchronous -calculus, but not in an asynchronous one =-=[21]-=-. However, to see how much everything depends on the denition, in [10] the leader election problem has been solved using asynchronous CSP (ACSP). Thus it is not safe to claim that synchronous is more ... |

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Citation Context ...le given operational constraints. The approach is known under a variety of names, including AEexible computation [14], anytime algorithms [3], imprecise-computation [16], or design-to-time scheduling =-=[11]-=-. Anytime algorithms together with closely related decisiontheoretic metareasoning are two new promising techniques and their application to general decision-making architectures has not yet been inve... |

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Citation Context ...per, we concentrate on the problem of expressiveness of $- calculus. We demonstrate that $-calculus can express formalisms which have richer behavior than Turing machines: including cellular automata =-=[1]-=-, interaction machines [2426], neural networks, and random automata networks [12]. We believe that such expressive power is needed to tackle with construction universality, self-reproduction, and evol... |

57 |
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Citation Context ...ate that $-calculus can express formalisms which have richer behavior than Turing machines: including cellular automata [1], interaction machines [2426], neural networks, and random automata networks =-=[12]-=-. We believe that such expressive power is needed to tackle with construction universality, self-reproduction, and evolution problems. We present basic $-calculus constructs needed to support these cl... |

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Citation Context ...Theorem 33 Every process realizable on Turing machine (by -calculus) can be implemented by some -calculus process, which in turn can be implemented by some $-calculus process, i.e. TM ` C ` $C (1) In =-=[26]-=- it is claimed that Turing Machines are too weak to express interaction of object-oriented and distributed systems, and Interaction Machines (IMs) are proposed as a stronger model that better captures... |

13 | Coinductive Models of Finite Computing Agents
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Citation Context ... we can encode -calculus and -calculus. Next we will show that $-calculus can express formalisms which have richer behavior than Turing machines: including cellular automata [1], interaction machines =-=[24,25,27,28,13]-=-, neural networks, and automata networks [12], exactly due to allowing innite (but enumerable) application of the parallel composition operator. Example 31 Encoding of the -calculus Because $-calculus... |

7 |
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Citation Context ...d stabilizing ioe it is an integer. A TM cannot solve this problem since the real number can be given as 0.999..., and hence TM will not even nish reading its input in nite time). Theorem 37 TM ae CA =-=(5)-=- Expressiveness of $-Calculus: What Matters? 9 Formally, an automata network [12] is a pair (D; fM i g) consisting of a cellular space (D; fQ i g) (countably innite, locally-nite directed graph D with... |

6 |
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Citation Context ...parallel computation, including -calculus [2] and -calculus [1820]. The $-calculus leads to a new programming paradigm: cost languages, and a new class of computer architectures: cost-driven machines =-=[4]-=-. In this paper, we concentrate on the problem of expressiveness of $- calculus. We demonstrate that $-calculus can express formalisms which have richer behavior than Turing machines: including cellul... |

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(Show Context)
Citation Context ... a new approach has found already several applications. It has been applied to the OOEce of Naval Research SAMON Project for coordination of multiple heterogeneous Autonomous Undersea Vehicles (AUVs) =-=[8,9]-=-. The Generic Behavior Message-Passing Language (GBML) has 12 Eugene Eberbach been derived from $-calculus for communication and script design of multiple cooperating mobile robots. $-calculus is also... |

5 |
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Citation Context ...work by ( k i (ffi i x i x i 1 ::: x i d i )). Summarizing, from the last result and from (4),(5) we obtain the following hierarchy of expressiveness of the models. Theorem 38 TM ae CA ` NN ` AN ` $C =-=(6)-=- If to allow innitary concepts in -calculus (probably, the most important - an innite unbounded parallel composition and true concurrency), then - calculus could also express interaction machines, cel... |

3 |
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Citation Context ... a new approach has found already several applications. It has been applied to the OOEce of Naval Research SAMON Project for coordination of multiple heterogeneous Autonomous Undersea Vehicles (AUVs) =-=[8,9]-=-. The Generic Behavior Message-Passing Language (GBML) has 12 Eugene Eberbach been derived from $-calculus for communication and script design of multiple cooperating mobile robots. $-calculus is also... |

3 |
The Polyadic -Calculus: A Tutorial, in F.L.Bauer,W.Brauer (eds.) Logic and Algebra of Specif ication
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Citation Context ... of the higher-order features, we could also encode higher-order -calculus (HO) in $-calculus. We assume that in a function denition, a function name can be either a constant or a variable. Sangiorgi =-=[23,19]-=- has proved that higher-order -calculus is not more expressive than (rst-order) -calculus. Thus such simulation becomes superAEuous. From the above and Milner in [19] showed has to simulate -calculus ... |

2 | Calculus: Flexible Optimization and Adaptation under Bounded Resources - Eberbach, Brooks - 1999 |

2 |
Interactive Software Technology, in: The Computer Science and Engineering Handbook
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(Show Context)
Citation Context ... we can encode -calculus and -calculus. Next we will show that $-calculus can express formalisms which have richer behavior than Turing machines: including cellular automata [1], interaction machines =-=[24,25,27,28,13]-=-, neural networks, and automata networks [12], exactly due to allowing innite (but enumerable) application of the parallel composition operator. Example 31 Encoding of the -calculus Because $-calculus... |

2 |
Interaction, Computability, and Church's Thesis, Accepted to the British Computer Journal (also http://www.cs.umb.edu/dqg
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Citation Context |

1 |
A Proof System for Asynchronously Communicating
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(Show Context)
Citation Context ...-calculus. Then, for instance, the leader election problem can be solved in synchronous -calculus, but not in an asynchronous one [21]. However, to see how much everything depends on the denition, in =-=[10]-=- the leader election problem has been solved using asynchronous CSP (ACSP). Thus it is not safe to claim that synchronous is more expressive than asynchronous unless we precisely dene both notions. Do... |