## 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

3697 |
Artificial Intelligence : A Modern Approach
- Russell, Norvig
- 1995
(Show Context)
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... |

1329 | A calculus of communicating systems - Milner - 1980 |

497 |
An Analysis of Time-dependent Planning
- Dean, Boddy
- 1988
(Show Context)
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... |

320 |
The Calculi of Lambda Conversion
- Church
- 1941
(Show Context)
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... |

258 |
Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms
- Sangiorgi
- 1992
(Show Context)
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 ... |

225 | On-line algorithms for scheduling imprecise computations
- Shih, Liu
- 1996
(Show Context)
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 ... |

222 | Why interaction is more powerful than algorithms
- Wegner
- 1997
(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... |

178 | Reasoning about beliefs and actions under computational resource constraints
- Horvitz
- 1987
(Show Context)
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... |

159 | A Calculus of Mobile - Milner, Parrow, et al. - 1992 |

154 | Comparing the expressive power of the synchronous and the asynchronouspi-calculus
- Palamidessi
- 1997
(Show Context)
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 ... |

112 | Design-to-Time Real-Time Scheduling
- Garvey, Lesser
- 1993
(Show Context)
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... |

73 |
Essays on Cellular Automata
- BURKS
- 1970
(Show Context)
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... |

56 |
Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks
- Garzon
- 1995
(Show Context)
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... |

27 | Persistent turing machines as a model of interactive computation - Goldin - 2000 |

14 |
Interactive Foundations of Computing", Theoretical Computer Science 192
- Wegner
- 1972
(Show Context)
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
- Wegner, Goldin
- 1999
(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... |

7 |
A Generic Tool for Distributed AI with Matching as Message Passing
- Eberbach
- 1997
(Show Context)
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 |
SEMAL: A Cost Language Based on the Calculus of Self-modifiable Algorithms
- Eberbach
- 1994
(Show Context)
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... |

6 | SAMON: communication, cooperation and learning of mobile autonomous robotic agents
- Eberbach, Phoha
- 1999
(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 |
Enhancing Genetic Programming by $-calculus, Proc. of the Second Annual Genetic Programming Conference GP-97
- Eberbach
- 1997
(Show Context)
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 |
Flexible Optimization and Evolution of Underwater Autonomous Agents
- unknown authors
- 1999
(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... |

3 |
The Polyadic -Calculus: A Tutorial, in F.L.Bauer,W.Brauer (eds.) Logic and Algebra of Specif ication
- Milner
- 1992
(Show Context)
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
- Wegner
- 1997
(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
- Wegner, Goldin
- 1999
(Show Context)
Citation Context |

1 |
A Proof System for Asynchronously Communicating
- Francez, Stomp
- 1993
(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... |