R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conference on Artificial Intelligence, pages 481--489. British Computer Society, September 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....definitions. Definition 27 For abstraction relation, R Sigma Theta Sigma A , a model, M Sigma , is R simulated by A Sigma A iff for all s 2 Sigma, a 2 Sigma A , 2 M, s R a and (0) s imply there exists 2 A such that (0) a and R The notion of simulation is the usual one [32]: when s R a, then every trace in M starting at s is reproduced by a corresponding trace in A that starts at a. This property implies universal soundness: Theorem 28 If R Sigma Theta Sigma A reflects atomic properties (that is, s R a implies I(s) IA A , then for all a 2 Sigma A ; s 2 ....

R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conf. on Artificial Intelligence. British Computer Society, 1971. 52

....the model ## , namely # # and # # .These reduced structures are constructed via data abstraction [22] and (by a result proved in [23] any property that can be shown to hold for a reduced model, holds for the concrete model. It can be shown that for any # # # there is a simulation preorder [24] between # and # #### . Similarly, for all # # #,forall # # ###### ##, there is a simulation preorder between # and # ### # . For models # and # , # ## # implies that ### #. Proof of theorem 1 follows. When # # is property 4, we can show, using model checking, that # #### ## # # and ....

R. Milner, "An algebraic definition of simulation between programs," in Proceedings of the 2nd International Joint Conference on Artificial Intelligence, 1971, pp. 481--489.

....the logic L # that, like those in the untimed setting and unlike that o#ered in [19] yield formulae whose size is linear with respect to that of the timed automaton they characterize. We present characteristic formula constructions for timed bisimilarity [28] timed versions of the simulation [21] and ready simulation [5, 20] preorders and for the faster than preorder [23] In particular, the characteristic formula construction for timed bisimilarity improves upon that o#ered in [19] In addition, since, if B is a deterministic timed automaton, checking whether the set of timed traces ....

R. Milner, An algebraic definition of simulation between programs, in Proceedings 2 Joint Conference on Artificial Intelligence, William Kaufmann, 1971, pp. 481--489. Also available as Report No. CS-205, Computer Science Department, Stanford University.

....of a class in which one can store elements from A, which reappear at some unspecified later stage 5 Refinements with invariant and bisimulation proofs A refinement establishes a relation between two specifications. Usually one says that an abstract specification is refined by a concrete one, see [9, 21, 4] (and also Section 2) This means that the behaviour that is specified in the abstract specification can be realised by the concrete specification. The latter often contains more details about how to realise this behaviour. Typically, it is more deterministic (i.e. less underspecified) than the ....

R. Milner. An algebraic definition of simulation between programs. In Sec. Int. Joint Conf. on Artificial Intelligence, pages 481--489. British Comp. Soc. Press, London, 1971.

....in stating whether the concrete fixed point is contained or contains a given property. This is the question of the correctness of the applied abstraction. There exist two closely related frameworks for developing abstractions and proving their correctness. The framework of simulation [Par81,Mil71] is about structural relation between abstract and concrete transition systems, representing the step relation of programs by means of an abstraction relation between abstract and concrete sets of states, where each concrete (set of transitions) transition must be simulatable by an abstract ....

....technique for pushing further the limits of model checking: given a program and a property to be verified, find a (simpler) abstract program such that the satisfaction on the abstract program implies the satisfaction on the initial program, called concrete program. Simulation as defined by Milner [Mil71] yields an appropriate preorder. In section 4.2, we introduce the notions of abstraction and property preservation and show that, given some invariant, a weaker notion of simulation, imposing no requirement on the successors of states outside the invariant, preserves the same set of properties. ....

[Article contains additional citation context not shown here]

R. Milner. An algebraic definition of simulation between programs. In Proc. Second Int. Joint Conf. on Artificial Intelligence, pages 481--489. BCS, 1971.

....the model MN , namely M N and M N . These reduced structures are constructed via data abstraction [22] and (by a result proved in [23] any property that can be shown to hold for a reduced model, holds for the concrete model. It can be shown that for any N 3 there is a simulation preorder [24] between M and M Abs0 . Similarly, for all i 1, for all N max(i; 4) there is a simulation preorder between M and M Abs i . For models M and M , M j= implies that M j= Proof of theorem 1 follows. When i is property 4, we can show, using model checking, that M Abs0 j= 0 ....

R. Milner, "An algebraic definition of simulation between programs," in Proceedings of the 2nd International Joint Conference on Artificial Intelligence, 1971, pp. 481--489.

.... return n.getlt0; Fig. 1. Toy example of FIFO queue. In previous work [3] we formulated a semantic notion of ownership and proved that it is a suciently strong invariant to justify modular reasoning about equivalence of class imple mentations using the standard notion of simulation [18, 13, 21, 11]. This notion of ownership has several restrictions that make it inflexible in ways similar to some of the earlier propos als [14, 15] One restriction is that encapsulated representation objects may not have outgoing references to clients of the owner. In the full version [2] of [3] this ....

R. Milner. An algebraic definition of simulation between programs. In Proceedings of Second Intl. Joint Conf. on Artificial Intelligence, pages 481-489, 1971.

.... of a language with only first order functions, it is usually enough to use an invariant on the domain of concrete values together with a function mapping concrete values (that satisfy the invariant) to abstract values [Hoa72] but a strictly more general method is to use a homomorphic relation [Mil71], Sch90] ST97] If non determinism is present in the language then some kind of bisimulation relation is required. This research was partly supported by the MRG project (IST 2001 33149) which is funded by the EC under the FET proactive initiative on Global Computing. SK was supported by an ....

R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence. British Computer Society, 481--489 (1971).

.... flights flight number [ AF1 ] flight number [ AF2 ] 5.2 Rooted Simulation A notion of rooted simulation is used below in Section 5.3 in formalising the satisfaction of semistructured expressions and atomic formulas in an interpretation. The following definition is inspired from [7,8] and refines the simulation considered in [9] Recall that a (directed) rooted graph G (V, E, r) consists in a set V of vertices, a set E of edges (i.e. ordered pairs of vertices) and a vertex r called the root of G such that there is in G a path from r to each vertex of G. Definition 1 (Rooted ....

Milner, R..: An Algebraic Definition of Simulation between Programs. Memo aim- 142, Stanford Univ. (1971)

....start investigating the resulting notions of substitutability. In Section 4, we take a first step in this direction, by showing the connection between behavioral inheritance and the classical refinement notions of trace containment and simulation from the literature on the semantics of concurrency [15]. From this connection, we deduce the computational complexity of some relevant algorithmic problems, such as deciding whether one class is substitutable for another. There has been a related effort at defining substitutability in OOAD, which is described in [17] 22] Like our approach here, ....

....1, create, EGG, rain) BOILING COOK, 1, prepare) BOlLING COOK, 2, destroy, EGG, max) HUMAN (destroy, EGG, prepare (EGG, max, fry) create, EGG, destroy, EGG, prepare (EGG, max, boil) FRYING COOK BOILING COOK EGG Fig. 4. 2 c , yet 2 : not vice versa [15]. As illustrated in Example 3.2, this is true for our object systems too: Proposition 3.3. Branching substitutability implies linear substitutability, but not vice versa. We note, however, that as with state transition graphs, when all the components of the systems are instances of ....

R. Milner, "An Algebraic Definition of Simulation between Programs," Proc. Second Int'l Joint Conf. Artificial Intelligence, pp. 481-489, Sept. 1971.

....is a relation # A B that is closed under the operations and is the identity on A bool = B bool . Two algebras A, B Mod (#) are observationally equivalent, written A B, if there exists a correspondence between them. This formulation is due to [Sch87] cf. simulations in [Mil71] and weak homomorphisms in [Gin68] and is equivalent to other standard ways of defining observational equivalence between algebras, where a special role is played by observable equalities, i.e. equalities between terms of observable sorts. For any specification SP with Sig(SP) #, we ....

R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence, London, 481--489 (1971).

....eternity variables as an alternative for prophecy variables. We first extend the conceptual framework by unifying the ideas of refinement mapping and extension with history variables or prophecy variables to the concepts of simulation. Actually, the term simulation has been introduced by Milner [12] in 1971. He used it for a kind of relation, which was later called downward or forward simulation to distinguish it from so called upward or backward simulation [4, 11] It seems natural and justified to reintroduce the term simulation for the common generalization. We then introduce eternity ....

....prove that one specification simulates (the behaviour of) another is by starting at the beginning and constructing the corresponding behaviour in the other specification inductively. This requires a condition embodied in so called forward or downward simulations [4, 11] which go back at least to [12]. They are defined as follows. A relation F between states(K) and states(L) is defined to be a forward simulation from specification K to specification L i# (H0) For every x init(K) there is y init(L) with (x, y) F . H1) For every pair (x, y) F and every x # with (x, x # ) ....

Milner, R.: An algebraic definition of simulation between programs. In: Proc. 2nd Int. Joint Conf. on Artificial Intelligence. British Comp. Soc. 1971. Pages 481--489.

....them. That is, for f : s1 . sn s, a1 # A s 1 , an # A sn and b1 # B s 1 , bn B sn , if (a1 , b1 ) #s 1 , an , bn ) #sn then (fA(a1 , an) fB (b1 , bn) #s . 9 This formulation is due to [Sch87] cf. simulations in [Mil71] and weak homomorphisms in [Gin68] and is equivalent to other standard ways of defining observational equivalence between algebras, where a special role is played by observable equalities, i.e. equalities between terms of observable sorts. It is easy to check that identities are ....

R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence, London, 481--489 (1971).

....are refinements. Refinements are similar to the homomorphism between automata in the sense of classical automata theory [10] and to the data refinements that are used in program development to replace abstract mathematical data structures by concrete structures that are more easily implemented [40, 15, 30, 18]. Lamport [28] advocates the use of refinements to prove that one concurrent program module implements another. A refinement from an automaton A to another automaton B is a function from states of A to states of B such that (a) the image of every start state of A is a start state of B, and (b) ....

R. Milner. An algebraic definition of simulation between programs. In Proceedings 2 nd Joint Conference on Artificial Intelligence, pages 481--489. BCS, 1971.

....[9] from the abstract to the concrete system have been given. In the framework of process algebras, the problem of property preserving preorders and equivalences has also been widely studied. In this framework, the notions of abstractions are generally defined in terms of variants of simulation [31] and bisimulation [32] the problem of the construction of abstract programs has only been addressed for notions of abstractions defined by equivalences. In the linear semantics framework, the intuitive notion of abstraction is inclusion (respectively equality) of observable computation sequences ....

.... in [40] 41] We define a notion of abstraction on transition systems as a simulation parameterized by Galois connections (ff; fl) We show that the notion of abstraction induced by hff; fli simulation coincides exactly with the notion of abstraction defined by simulation in the sense of Milner [31], parameterized by the relation ae corresponding to the Galois connection (ff; fl) Then, we give preservation results for fragments of a future and past version of the branching time calculus defined in [24] for the following notion of property preservation : an arbitrary function ff from the ....

[Article contains additional citation context not shown here]

R. Milner. An algebraic definition of simulation between programs. In Proc. Second Int. Joint Conf. on Artificial Intelligence, pages 481--489. BCS, 1971.

....to a wide variety of logics such as branching time logics [CE 81, QS 82, EL 86] and linear time logic [LP 85] and to a variety of programming models such as finite state programs [CE 81, QS 82] and real time systems [ACD 90] 2. 6 Equivalences on Transition Systems The notions of simulation [Milner 71] and bisimulation [Park 81, Milner 90] are the basic ways of comparing the structure of transition systems. There are several variants; an important one being bisimulation under stuttering (finite repetition) of state labelings [BCG 88, dNV 90, Milner 90] We present here the three main notions ....

Milner, R. An Algebraic Definition of Simulation Between Programs, Proceedings of the 2nd International Joint Conference on Artificial Intelligence, William Kaufmann, September 1971.

....: l i , 9i : l i , 8i : l i , 9i : l i and 9i 6= j : l i l j . For example, AG: 9i 6= j : C i C j ) is a formula of ASCTL . 2.1 Simulation up to Permutation Let M = S; R) and M = S ) be structures defined over LP and I . B S Theta S is a simulation up to permutation (c.f. [Mi71] [Pa81] HM85] MAV96] ES96] CEFJ96] iff for all (s; s ) 2 B ffl there is a 2 Sym I such that (s) s and ffl for all (s; t) 2 R there is a t such that (s and (t; t ) 2 B. B S Theta S is a bisimulation up to permutation iff for all (s; s ) 2 B the above two ....

Milner, R., An Algebraic Definition of Simulations Between Programs. In Proceedings of the Second International Joint Conference on Artificial Intelligence, British Computer Society, 1971, pp 481-489.

....variables as an alternative for prophecy variables. We first extend the conceptual framework by unifying the ideas of refinement mapping and extension 2 with history variables or prophecy variables to the concepts of simulation. Actually, the term simulation has been introduced by Milner [12] in 1971. He used it for a kind of relation, which was later called downward or forward simulation to distinguish it from so called upward or backward simulation [4, 11] It seems natural and justified to reintroduce the term simulation for the common generalization. We then introduce eternity ....

....prove that one specification simulates (the behaviour of) another is by starting at the beginning and constructing the corresponding behaviour in the other specification inductively. This requires a condition embodied in so called forward or downward simulations [4, 11] which go back at least to [12]. They are defined as follows. A relation F between states(K) and states(L) is defined to be a forward simulation from specification K to specification L i# (H0) For every x start(K) there is y start(L) with (x, y) H1) For every pair (x, y) F and every x # with (x, x # ) ....

Milner, R.: An algebraic definition of simulation between programs. In: Proc. 2nd Int. Joint Conf. on Artificial Intelligence. British Comp. Soc. 1971. Pages 481--489.

....liveness(f) Example The tableau for f = AG(p#AX(A p 1 U p 2 ) is shown in Figure 1 on the following page. The initial states are 0 and 1, and the fairness condition is pos f #= 1#pos f #= 4#pos f #= 5 . We can characterize satisfaction of an ACTL formula f by the simulation order (see [19, 5]) between a Kripke structure and the tableau T f . This use of the simulation order was introduced by Long [15] Let S = Q,Q 0 , R,F) be a Kripke structure and T f = Q f , Q 0f , R f , F f ) the tableau for an ACTL formula f. A relation ##QQ f is a simulation of S by T f if the following ....

R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conference on Artificial Intelligence, pages 481--489, September 1971.

....) fj is a computation path in Mg. In LTL, if M 6j= then there is a computation path in M , such that fg 6j= Using the same arguments as in the proof of claim 19, we can show that a counterexample to will always be a model with one computation path in it. CTL and CTL : Milner in [Mil71] has proved that for CTL and CTL , the natural pre order is: M 1 OE CTL M 2 iff M 1 bi simulates M 2 . This means that CTL and CTL have only trivial counter examples that are the model itself. Indeed, the formula EF (p) cannot be shown false by any model that has less behavior than the ....

....states where p was true. Note that even if we did have some method of specifying larger models as counter examples, CTL would still be problematic. The formula EF (p) AG(q) cannot be proved false using neither a larger model, nor a smaller one. ACTL and ACTL : Using the same proof as in [Mil71], it can be shown that for ACTL and ACTL , the natural pre order is: M 1 OE ACTL M 2 iff M 2 simulates M 1 . For these logics, it is difficult to characterize counter examples. A model M always simulates a computation path in it ( OE ACTL M ) meaning that computation paths may serve as ....

R. Milner. "An Algebraic Definition of Simulation between Programs", In Proc. 2nd International Joint Conference on Artificial Intelligence, British Computer Society, September 1971.

....i , 9i : l i , 8i : l i , 9i : l i and 9i 6= j : l i l j . For example, AG: 9i 6= j : C i C j ) is a formula of SACTL . 2.1 Simulation up to Permutation Let M = S; R) and M 0 = S 0 ; R 0 ) be structures defined over LP and I. B S Theta S 0 is a simulation up to permutation (cf. [Mi71] [Pa81] HM85] MAV96] ES96] CE 96] iff for all (s; s 0 ) 2 B there is a 2 Sym I such that (s) s 0 and for all (s; t) 2 R there is a t 0 such that (s 0 ; t 0 ) 2 R 0 and (t; t 0 ) 2 B. B S Theta S 0 is a bisimulation up to permutation iff for all (s; s 0 ) 2 B ....

Milner, R., An Algebraic Definition of Simulations Between Programs. In Proceedings of the Second International Joint Conference on Artificial Intelligence, British Computer Society, 1971, pp 481-489.

....method is determined by the nature of the relationship between the concrete and the abstract program. A typical relationship is that the abstract program is able to match every computation of the concrete program. This is formalized in the definitions below. Definition 0 (Simulation Relation) Mil71] A relation R S Theta S is a simulation relation on a TS M = S; Delta; I ; AP; L) iff for any (s; t) 2 R, L(s) L(t) and for any u such that s Gamma u, there exists v such that t Gamma v and (u; v) 2 R. 1 The usual unconditional, weak and strong fairness conditions can be written as ....

R. Milner. An algebraic definition of simulation between programs. In 2nd IJCAI, 1971.

....to a specification state of Q. This tighter relation is captured mathematically by the notion of a simulation relation. Intuitively, Q simulates P iff, starting from the initial states and continuing ad infinitum, every inputoutput pair of P can be matched by the same input output pair in Q [Mil71]. Clearly, if Q simulates P , then every trace of P is also a trace of Q. The converse is not true; that is, simulation is a stronger requirement than trace containment. However, it has been said that trace containment without simulation is more often than not due to coincidence rather than ....

R. Milner. An algebraic definition of simulation between programs. In Proceedings of the 2nd International Joint Conference on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

....setting. Another approach to modular verification for 8CTL is proposed in [43] where the following inference rule is proposed: M 1 A 1 A 1 jjM 2 A 2 M 1 jjA 2 j= 9 = M 1 jjM 2 j= Here A 1 and A 2 are modules that serve as assumptions, and is the simulation refinement relation [75]. In other words, if M 1 guarantees the assumption A 1 , M 2 under the assumption A 1 guarantees the assumption A 2 , and M 1 under the assumption A 2 guarantees , then we know that M 1 jjM 2 , under no assumption, guarantees . The advantage of this rule is that both the and j= relation can ....

R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conference on Artificial Intelligence, pages 481--489. British Computer Society, September 1971.

....efficiency. Nevertheless, we provide evidence that the technique is useful in practice through some examples. 1. 1 Background State relations in one form or another have been studied for a long time, including the weak homomorphisms and coverings of Ginzburg [Gin68] and the simulations of Milner [Mil71]. Many verification methods consider (possibly) infinite state automata, and therefore develop proof methodologies where the human verifier supplies a relation together with a mathematical proof that it is a simulation relation (for example, Milner s simulations, Lam and Shankar s protocol ....

R. Milner, "An algebraic definition of simulation between programs", Proceedings of the 2nd International Joint Conference on Artificial Intelligence, British Computer Society, 1971, pp. 481--489.

....were in contexts where there was no independent informationhiding mechanism (like our units) and therefore the problems addressed in the present paper did not arise, or were ignored in the semi formal treatments in the literature. These treatments include Milner s definition of simulation [37], Hoare s classic treatment of abstraction functions [18] and the influential work of Liskov and Guttag and the rest of the CLU community [35] The first programming language to support information hiding in the way our units do was Mesa [38] with its definition modules and implementation ....

Robin Milner. An algebraic definition of simulation between programs. Technical Report Stanford Artificial Intelligence Project Memo AIM-142, Computer Science Department Report No. CS-205, Stanford University, February 1971.

....p # implies that there is a transition q a # q # with p # R q # . For closed terms p, q, we write p # # 1 q i# p R q with R a simulation. The kernel of # # 1 (i.e. the equivalence # # 1 #( # # 1 ) 1 ) is denoted by # 1 . The relation # # 1 is the well known simulation preorder [13]. Definition 2. For closed terms p, q, we write p # # 2 q i# p R q with R a simulation and R 1 included in # # 1 . The kernel of # # 2 (i.e. the equivalence # # 2 #( # # 2 ) 1 ) is denoted by # 2 . The relations # # 2 and # 2 are the 2 nested simulation preorder and the ....

R. Milner, An algebraic definition of simulation between programs, in Proceedings 2nd Joint Conference on Artificial Intelligence, William Kaufmann, 1971, pp. 481-- 489.

....we eventually reach a state from which, no matter how we continue, no requests are sent) as in 8CTL. In both cases, the more behaviors the system has, the harder it is for the system to satisfy the requirements. Indeed, universal temporal logics induce the simulation order between systems [Mil71, CGB86] That is, a system M simulates a system M 0 if and only if all universal temporal logic formulas that are satisfied in M 0 are satisfied in M as well. On the other hand, formulas of non universal temporal logics, such as CTL and CTL , may also impose possibilityrequirements on the ....

R. Milner. An algebraic definition of simulation between programs. In Proceedings of the 2nd International Joint Conference on Artificial Intelligence, pages 481--489, September 1971.

....to a specification state of Q. This tighter relation is captured mathematically by the notion of a simulation relation. Intuitively, Q simulates P iff, starting from the initial states and continuing ad infinitum, every inputoutput pair of P can be matched by the same input output pair in Q [Mil71]. Clearly, if Q simulates P , then every trace of P is also a trace of Q. The converse is not true; that is, simulation is a stronger requirement than trace containment. However, it has been said that trace containment without simulation is more often than not due to coincidence rather than ....

R. Milner. An algebraic definition of simulation between programs. In Proceedings of the Second International Joint Conference on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

....of all properties) We first apply model checking to verify that the specification formula is true for the implementation model. The formula is then transformed into a tableau [3] By definition, since the formula is true for the model, the tableau is greater by the simulation preorder [9] than the model. We defined a reduced tableau for ACTL safety formulas. Our tableau is based on the Particle tableau for LTL, presented in [6] We further reduce their tableau by removing redundant tableau states. We next use the simulation preorder to find differences between the implementation ....

....M satisfies a formula , denoted M j= if every initial state of M satisfies . Let M = S; S 0 ; R; L) and M 0 = S 0 ; S 0 0 ; R 0 ; L 0 ) be two Kripke structures over the same set of atomic propositions AP . A relation SIM S Theta S 0 is a simulation preorder from M to M 0 [9] if for every initial state s 0 of M there is an initial state s 0 0 of M 0 such that (s 0 ; s 0 0 ) 2 SIM . Moreover, if (s; s 0 ) 2 SIM then the following holds: L(s) L 0 (s 0 ) and 8s 1 [ s; s 1 ) 2 R = 9s 0 1 [ s 0 ; s 0 1 ) 2 R 0 (s 1 ; s 0 1 ) 2 SIM ] 1 ....

R. Milner. An algebraic definition of simulation between programs. In In proceedings of the 2nd International Joint Conference on Artificial Intelligence, pages 481--489, September 1971.

....mechanism to manage accesses to components not present in the classified object. In order to formally define the notion of weak membership and to define a method to check whether an object is a weak member of a class, we extend a well known theoretical notion, the simulation relation [16]. First, we provide an abstract representation of the structural type of a class, the class structural expression, and an abstract representation of the object state, the object value expression. Then, to verify whether the object is a weak member of the class, we check whether a particular ....

R. Milner. An Algebraic Definition of Simulation between Programs. In Proc. of the 2nd IJCAI, pages 481--489, London, UK, 1971.

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R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conference on Artificial Intelligence, pages 481--489. British Computer Society, September 1971.

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R. Milner. An algebraic definition of simulation between programs. In International Joint Conference on Artificial Intelligence, pages 481--489. Kaufmann, 1971. 3

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R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd Int. Joint Conf. on Artif. Int., pages 481--489. British Computer Society, September 1971.

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R. Milner. An algebraic definition of simulation between programs. In Proc. of the 2nd International Joint Conference on Artificial Intelligence, pages 481--489, 1971.

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R. Milner. An algebraic definition of simulation between programs. In Second International Joint Conference on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

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R. Milner. An algebraic definition of simulation between programs. In Second International Joint Conference on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

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R. Milner. An algebraic definition of simulation between programs. In Proc. of the 2nd International Joint Conferences on Artificial Intelligence (IJCAI), pages 481--489, London, UK, 1971.

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R. Milner. An algebraic definition of simulation between programs. Proc. IJCAI, pages 481--489, 1971.

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R. Milner. An algebraic definition of simulation between programs. In D. C. Cooper, editor, Proc. of the 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481--489, London, UK, September 1971. William Kaufmann. ISBN 0-934613-34-6. 37

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R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence, London, 481--489 (1971).

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R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence, London, 481--489 (1971).

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R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd Int. Joint Conf. on Artificial Intelligence, pages 481--489. British Comp. Soc., 1971.

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R. Milner. An algebraic definition of simulation between programs. In Proc. 2nd International Joint Conference on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

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R. Milner. An algebraic definition of simulation between programs. Proc. 2nd Intl. Joint Conf. on Artificial Intelligence. British Computer Society, 481--489 (1971).

No context found.

R. Milner. An algebraic definition of simulation between programs. Technical Report CS-205, Computer Science Dept, Stanford University, February 1971.

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Robin Milner. An algebraic definition of simulation between programs. In D. C. Cooper, editor, Proc. of the 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481--489, London, UK, September 1971. William Kaufmann.

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R. Milner. An algebraic definition of simulation between programs. In Proc. of Second Int. Joint Conf. on Artificial Intelligence, pages 481--489. The British Computer Society, 1971.

No context found.

R. Milner. An algebraic definition of simulation between programs. In Sec. Int. Joint Conf. on Artificial Intelligence, pages 481--489. British Comp. Soc. Press, London, 1971.

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R. Milner, An algebraic definition of simulation between programs, in Proceedings 2nd Joint Conference on Artificial Intelligence, William Kaufmann, 1971, pp. 481-- 489.

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