## Time and Information in Sequential and Concurrent Computation (1994)

### Cached

### Download Links

- [boole.stanford.edu]
- [boole.stanford.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proc. Theory and Practice of Parallel Programming |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Pratt94timeand,

author = {Vaughan Pratt},

title = {Time and Information in Sequential and Concurrent Computation},

booktitle = {In Proc. Theory and Practice of Parallel Programming},

year = {1994},

pages = {1--24}

}

### OpenURL

### Abstract

Time can be understood as dual to information in extant models of both sequential and concurrent computation. The basis for this duality is phase space, coordinatized by time and information, whose axes are oriented respectively horizontally and vertically. We fit various basic phenomena of computation, and of behavior in general, to the phase space perspective. The extant two-dimensional logics of sequential behavior, the van Glabbeek map of branching time and true concurrency, event-state duality and schedule-automaton duality, and Chu spaces, all fit the phase space perspective well, in every case confirming our choice of orientation. 1 Introduction Our recent research has emphasized a basic duality between time and information in concurrent computation. In this paper we return to our earlier work on sequential computation and point out that a very similar duality is present there also. Our main goal here will be to compare concurrent and sequential computation in terms of this dua...

### Citations

469 |
The mathematics of sentence structure
- Lambek
- 1958
(Show Context)
Citation Context ...e b / a is dually called the left residual of b by a. Such logics add implication to the language. These are the Ajdukiewicz monoids [Ajd37], brought to greater prominence two decades later by Lambek =-=[Lam58]. The term-=- residuation was coined by Ward and Dilworth [WD39]. That the binary relations on a set formed a residuated ISR was first observed by De Morgan as his "Theorem K" [DM60]. The subclass BSR of... |

275 |
The Logic of Quantum Mechanics
- Birkhoff, Neumann
- 1936
(Show Context)
Citation Context ...b], although the details of this second point of contact have only become clear to us since then. These connections get considerably closer to the essence of quantum mechanics than does quantum logic =-=[BvN36]-=-, which abstracts away from complementarity to capture just the underlying projective geometry of quantum mechanics. Quantum logic is to Chu spaces as nonconstructive methods of mathematics are to con... |

214 | Semantical considerations on FloydHoare logic
- Pratt
- 1976
(Show Context)
Citation Context ...om sequential to concurrent behavior began with the basic step of replacing binary relations, as sets of state transitions (as used by Park and Hitchcock [HD73], DeBakker and deRoever [dBdR72], Pratt =-=[Pra76]-=-, etc.), by processes as sets of traces [HL74]. This refinement permits the definition of concurrent composition as the interleaving or shuffle of traces. However this model is global as noted above w... |

87 |
autonomous category and linear logic
- Barr
- 1991
(Show Context)
Citation Context ...ver the twoelement set 2 = f0; 1g. Chu spaces have an equally evident duality obtained by transposition, which has the side effect of reversing the direction of the Chu transforms. As noticed by Barr =-=[Bar91]-=- and further developed by several authors [dP89, BG90, LS91, BGdP91, Pra93b], Chu spaces provide a straightforward interpretation of full linear logic; the fact that Set (as well as Pos and other even... |

83 |
Fundamentals of a Theory of Asynchronous Information Flow
- Petri
- 1962
(Show Context)
Citation Context ...valued time relative to the start of the trace. This particular type of refinement does not change the global nature of either the time or the information. The oldest model of concurrency, Petri nets =-=[Pet62]-=-, made both time and information local, at a time when there was very little modeling of even sequential behavior in computer science. Setting Petri nets to one side for the moment, the progression fr... |

57 |
R.P.: Residuated Lattices
- Ward, Dilworth
- 1939
(Show Context)
Citation Context ...ics add implication to the language. These are the Ajdukiewicz monoids [Ajd37], brought to greater prominence two decades later by Lambek [Lam58]. The term residuation was coined by Ward and Dilworth =-=[WD39]. That the-=- binary relations on a set formed a residuated ISR was first observed by De Morgan as his "Theorem K" [DM60]. The subclass BSR of Boolean semirings has the property that the semilattice stru... |

55 | Origins of the calculus of binary relations - Pratt - 1992 |

50 | Action logic and pure induction - Pratt - 1990 |

49 | Chu Spaces: A Model of Concurrency - Gupta - 1994 |

48 | A categorical linear framework for Petri nets, in - Brown, Gum - 1990 |

48 | Games Semantics for Linear Logic - Lafont, Streicher - 1991 |

47 |
A calculus of communicating systems, LNCS92
- Milner
- 1980
(Show Context)
Citation Context ...eginning this was much less clear, and each objector tended to focus on just one of these limitations. We now describe each of these types of objection. 2.4 Branching Time as Local Information Milner =-=[Mil80]-=- was the first to spell out a notion of local information, which soon became known as branching time to distinguish it from the linear time of the trace model. Milner proposed synchronization trees as... |

43 |
On partial languages
- Grabowski
- 1981
(Show Context)
Citation Context ...y ordered sets of events in which each event is labeled with the action of which it is an occurrence, one relaxes this linear order to a partial order to arrive at what has been called a partial word =-=[Gra81]-=- and a partially ordered multiset [Pra82] or pomset, the term now used. In a pomset with two occurrences of action a, an occurrence of b may be comparable with one of the a's and incomparable with the... |

36 |
Curriculum Process
- Wheeler
- 1967
(Show Context)
Citation Context ...ent is labeled with the action of which it is an occurrence, one relaxes this linear order to a partial order to arrive at what has been called a partial word [Gra81] and a partially ordered multiset =-=[Pra82]-=- or pomset, the term now used. In a pomset with two occurrences of action a, an occurrence of b may be comparable with one of the a's and incomparable with the other, not possible with Mazurkiewicz tr... |

32 | Gages accept concurrent behavior
- Gupta, Pratt
- 1993
(Show Context)
Citation Context ...With suitable care in the definition of projection we may accomplish the same for biextensional Chu spaces, namely those having no repeated rows or columns, via a process we have previously described =-=[GP93]-=-, which we sketch briefly here. We project onto the information axis to yield an automaton in two steps. First close the rows of the Chu space under arbitrary union and intersection (OR and AND of the... |

31 |
A Calculus for Recursive Program Schemes
- Bakker, Roever
- 1973
(Show Context)
Citation Context ...e progression from sequential to concurrent behavior began with the basic step of replacing binary relations, as sets of state transitions (as used by Park and Hitchcock [HD73], DeBakker and deRoever =-=[dBdR72]-=-, Pratt [Pra76], etc.), by processes as sets of traces [HL74]. This refinement permits the definition of concurrent composition as the interleaving or shuffle of traces. However this model is global a... |

28 | A linear specification language for Petri nets - Brown, Gurr, et al. - 1991 |

27 | A dialectica-like model of linear logic - Paiva - 1989 |

27 |
Induction rules and termination proofs
- Hitchcoek, Park
- 1973
(Show Context)
Citation Context ...to one side for the moment, the progression from sequential to concurrent behavior began with the basic step of replacing binary relations, as sets of state transitions (as used by Park and Hitchcock =-=[HD73]-=-, DeBakker and deRoever [dBdR72], Pratt [Pra76], etc.), by processes as sets of traces [HL74]. This refinement permits the definition of concurrent composition as the interleaving or shuffle of traces... |

27 | Relation algebras with transitive closure - Ng - 1984 |

22 |
On the syllogism, no. iv, and on the logic of relations
- Morgan
(Show Context)
Citation Context ...des later by Lambek [Lam58]. The term residuation was coined by Ward and Dilworth [WD39]. That the binary relations on a set formed a residuated ISR was first observed by De Morgan as his "Theore=-=m K" [DM60]-=-. The subclass BSR of Boolean semirings has the property that the semilattice structure forms a Boolean algebra; for this it suffices for an antimonotone operation of negation :a to exist and satisfy ... |

20 |
Consistent and Complementary Formal Theories of the Semantics of Programming Languages
- Hoare, Lauer
- 1974
(Show Context)
Citation Context ... the basic step of replacing binary relations, as sets of state transitions (as used by Park and Hitchcock [HD73], DeBakker and deRoever [dBdR72], Pratt [Pra76], etc.), by processes as sets of traces =-=[HL74]-=-. This refinement permits the definition of concurrent composition as the interleaving or shuffle of traces. However this model is global as noted above with respect to both information and time. The ... |

17 | The Duality of Time and Information
- Pratt
- 1992
(Show Context)
Citation Context ...ets analogous to a trace process as a set of traces, may be understood as a Petri net with no branching at places. 5 Linear Automata and Schedules We turn now to a point of view we developed recently =-=[Pra92]-=- as a simple setting in which time and information were dual. There we gave up all branching in both the time and information domains to reduce this duality to its simplest form. The essence of this d... |

16 | Linear Logic for Generalized Quantum Mechanics - Pratt - 1993 |

12 | Relation algebras with transitive closure, abstract 742-02-09 - Ng, Tarski - 1977 |

10 | Concurrent Kripke structures - Gupta - 1993 |

8 |
Concurrent program schemas and their interpretation
- Mazurkiewicz
- 1977
(Show Context)
Citation Context ...nt. 2.5 True Concurrency as Local Time The dual of local information is local time, popularly called true concurrency in Europe starting around 1987. Local time was addressed early on by Mazurkiewicz =-=[Maz77]-=-, who realized it in the form of a symmetric binary relation on the alphabet Act indicating causal independence of occurrences of those actions. This relation induces a congruence (with respect to Kle... |

8 | Chu spaces: Automata with quantum aspects - Pratt - 1994 |

4 | spaces: Complementarity and uncertainty in rational mechanics - Chu - 1994 |

3 | A roadmap of some two-dimensional logics
- Pratt
- 1992
(Show Context)
Citation Context ...itten value, from a more sophisticated one that permits simultaneous reading and writing with the expectation that the read will return a previously written value. 3 Two-Dimensional Logic We recently =-=[Pra94c]-=- defined a general notion of two-dimensional logic, into which various logics of action could be fitted. The significance of two-dimensional logics for the present paper is that their disjunction and ... |

2 |
Die syntaktische konnexitat. Studia Philosophica, I:1--27
- Ajdukewicz
- 1937
(Show Context)
Citation Context ...that b(b / a)sa; a ! b is called the right residual of b by a, while b / a is dually called the left residual of b by a. Such logics add implication to the language. These are the Ajdukiewicz monoids =-=[Ajd37]-=-, brought to greater prominence two decades later by Lambek [Lam58]. The term residuation was coined by Ward and Dilworth [WD39]. That the binary relations on a set formed a residuated ISR was first o... |

1 |
Computations of distributed systems, part 1: flow event structures and flow nets
- Boudol
- 1990
(Show Context)
Citation Context ...y. The former remembers the choice longer until after c, while the latter forgets it before c, a distinction drawn by conventional (finite) state automata as well as by Boudol's flow event structures =-=[Bou90]-=-. The vertical axis therefore indicates the passage from global choice, where choice commitment and forgetting has no specific location in the computation, to local choice, that is, localized to speci... |