M. Minsky. Computation finite and infinite machines. Prentice-Hall, New Jersey, 1967.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....) of the uniform word problem for finitely presented commutative semigroups and a constant c 0 such that each derivation of m from m in P contains a word of length 2 c Deltas , where s denotes the input size. Using commutative semigroups to simulate counter or Minsky automata ([44]) this result implies (cf. 43] 7 requires exponential space, and is therefore, together with the matching upper bound, exponential space complete. Since the word problem for commutative semigroups is a special case of PIMP (the corresponding ideals are also called (pure difference) binomial ....

Marvin L. Minsky. Computation: Finite and infinite machines. Prentice-Hall, Englewood Cliffs, 1967.

....function. The functions that can be generated with all three rules are called partial recursive; if a function is total, i.e. defined for all x, it is simply recursive. The recursive functions turn out to correspond exactly to many other definitions of computability, including Turing machines [2], calculus, flowchart programs, Post s tag system, and so on [1] For this reason this class of functions is considered a deep and universal definition of computability; this is the Church Turing Thesis. To get larger classes of functions, we can extend our model of computation with oracles, ....

Marvin Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

....sented as a lecture at the Pan American Symposium of Applied Mathematics, Buenos Aires, Argentina, August 1968. The author is at Mario Bravo 249, Buenos Aires, Argentina. Their papers appear in Davis [1] As general references on computability theory we may also cite Davis [2] 4] Minsky [5], Rogers [6] and Arbib [7] the successive digits of #. Indeed, it is now generally accepted that any calculation that a modern electronic digital computer or a human computer can do, can also be done by such a machine. Section II How much information must be provided to a computer in order ....

M. Minsky, Computation: Finite and Infinite Machines. Englewood Cli#s, N.J.: Prentice-Hall, 1967.

....unification classes see [45, 51] In this paper we will show that the two problems are undecidable for append like programs. The proof technic of [19, 20] is based on an original encoding of the unpredictable iterations of J. Conway within number theory [8] which are close to Minsky machines [39]. An alternative proof of undecidability of the emptiness problem can be found in [28] It has been made independently and it is based on an encoding of the Post correspondence problem. We will present both proofs. We also study some particular subcases defined by the number of occurences of ....

....of the basic notions in the following sections. 4. MINSKY MACHINES AND CONWAY ITERATIONS In the following, the expression It is undecidable whether or not. stands for There exists no algorithm that always decides, whether or not. 4.1. Minsky Machines Presentation. The Minsky machines [39, 8] are deterministic machines with registers and instructions. Registers (finitely many of them) can hold arbitrary large non negative integers. A machine executes a program composed of instructions sequentially. Instructions are labeled by Q 1 , Q 2 , Delta Delta Delta, Qn (for a program of n ....

[Article contains additional citation context not shown here]

Minsky M. "Computation : Finite and Infinite Machines." Prentice--Hall. 1967.

....also provided with a program that contains a complete description of the Turing machine that it should simulate. Universal Turing machines can be constructed that are very small: Rogozhin [39] has made one version with 4 states and 6 symbols and one with only 2 states and 18 symbols, while Minsky [40] has one with 7 states and 4 symbols. Since the universal Turing machine must simulate the dedicated Turing machine it is often much slower than the Turing machine it simulates. But if the problem takes time t to solve using a dedicated Turing machine, the time needed for a universal Turing ....

M. L. Minsky, Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs, N.J., 1967.

....a one way input tape, and a finite number of integer counters. Each counter can be incremented by 1, decremented by 1, or stay unchanged. Besides, a counter can be tested against an integer constant. It is well known that counter machines with two counters have an undecidable halting problem [33], and obviously the undecidability holds for machines augmented with a pushdown stack. Thus, we have to restrict the behaviors of the counters. One such restriction is to limit the number of reversals a counter can make. A counter is n reversal bounded if it changes mode between nondecreasing and ....

M. L. Minsky, "Computation: finite and infinite machines," Prentice-Hall, 1967

....range to which the human mind has been applied. Simon Newell 1958) Simon and Newell weren t alone in their early optimism. For example, Marvin Minsky, another founder of AI, said in 1967: within a generation the problem of creating artificial intelligence will be substantially solved. (Minsky 1967) Understandably, people outside the field asked persistently are we there yet In the following two decades, the early hype turned to lost hope. By 1982, Minsky was quoted as saying that the AI problem is one of the hardest Copyright c 2002, Blank, Kumar, and Meeden. All rights reserved. ....

Minsky, M. 1967. Computation: Finite and Infinite Machines. Prentice-Hall.

....a labeled transition graph G satisfies a PD NBP P , denoted G j= P , if P accepts G. Theorem 6. The model checking problem for context free systems and pushdown path automata is undecidable. Proof. We do a reduction from the halting problem for two counter machines, shown to be undecidable in [Min67] to the problem of whether a context free graph satisfies a specification given by a PD NBP. In order to simulate the two counter machine by the context free system and the PD NBP, we use the state of the context free system (a word in V ) to maintain the value of the first counter, and we use ....

M.L. Minsky. Computation: Finite and Infinite Machines. Prentice Hall, 1967.

....of the difficultiness of these problems. First the commutation requirement, that is the fact that a word z is in the centralizer only if two specified local operations x Delta and Deltay together lead to another element of Z, resembles a computational step in tag systems of Post, cf. [12]. Second, the requirement is that, for all x in X, there must exist an y 2 X such the xzy is again in Z. In other words, we have a problem of 89 type, and such problems are in many cases known to be difficult. Despite of the above we would guess that the answer to Conway s Problem is ....

M. Minsky, Computation: Finite and Infinite Machines, Prentice Hall, 1967.

....have the form P (x; y) Q(c) where P (x; y) is as for HPCDs and Q(c) j c = 0 j c 0 j true. Resets are as for HPCDs, but they can also increment or decrement c. We prove that the reachability problem for HPCD 1c is undecidable showing that a HPCD 1c H can simulate Minsky (two counter) machines [28] for which reachability is known to be undecidable. Proposition 1 (HPCD 1c simulates MM) Every Minsky Machine M can be simulated by a 2 dim HPCD with one counter. Hence reachability is undecidable for HPCD 1c . Sketch of the proof: We associate with each q i of M a location i of HPCD 1c . In ....

M.L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

....queue is empty, halt; otherwise remove the leftmost symbol from the queue and write it to X) if X = a goto L, and halt, where L 0 is a label. A Queue program is a finite sequence of the form 1 : I 1 ; 2 : I 2 ; n : I n , where each I i is an instruction. By simulating Post s Tag Systems [12] in Queue, it is known that the problem QUEUE HALTING: Given a Queue program, will it halt eventually is undecidable. Given a Queue program P , we construct an IA program MP of the fragment in question that simulates P . Plainly the IA program MP eventually halts if and only if it is ....

M. L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

.... = 1; 2; k Gamma 1) is in one of the following two forms (assuming 1 l; l ; l k, 1 j m) ffl c j : c j 1; goto l ffl if c j = 0 then goto l else (c j : c j Gamma 1; goto l The halting problem is undecidable even for Minsky machines with two counters initialized to zero [21]. 6 3 The Tractability Border In this section we show that the problem whether a BPA process simulates a finite state one is PSPACE hard. The other preorder is shown to be co NP hard. Consequently, we also obtain co NP hardness of simulation equivalence between BPA and finite state processes. ....

M.L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

....in [1] and 1C is called iterated counter languages in [10] One turn counter machines are called reversal bounded in [9] The emptiness problem for PBLIND(n) is equivalent to the emptiness problem for PBLIND by adding an additional blank symbol replacing e moves. 2. According to Minsky [20, 21], cf. also [11, Sec. 7.8] the halting problem for two counter machines is undecidable, even if one takes D2C machines with only one accepting state whose counters never get below zero and to which is given the empty word as input. Such machines have a unique final configuration c f , i.e. C f ....

M. L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1971.

....When allowing non empty synchronization sets pom and loc become different. Theorem 16 For BPPH , loc ae pom ae lan Theorem 17 For BPPH , pom and loc are undecidable. Proof: It is well known that BPPH is Turing powerful, see e.g. 4] where it is shown how to simulate Minsky counter machines [21] in BPPH . Given the encoding of Minsky counter machines there is a standard way of reducing the halting problem for Minsky counter machines to an equivalence problem. Given a Minsky counter machine N first construct a BPPH process EN that simulates N and then another process FN that is an exact ....

M.L. Minsky, Computation - Finite and Infinite Machines, Prentice Hall (1967).

....by sim( x; y) x: y j xj:j yj (7) 2.2 Branch Network To do a finer temporal classification, the branch networks are composed of Elman recurrent neural networks [7] Figure 3 shows this layered partialrecurrent network structure. In 1967, Minsky made the following consequential claim [1]: Every finite state machine is equivalent to and can be simulated by some neural net Minsky s claim focused only on one specific neuron model (McCulloch and Pits neuron) and allowed arbitrary connections between neurons. In 1990, Elman proposed a simple recurrent network which is able to ....

M. Minsky, Computation: Finite and Infinite Machines, Englewood Cliffs, NJ: PrenticeHall, 1967

....is to decide whether S belongs to the optimal slice of # with respect to C. The slicing problem is parameterized by the class of programs considered. Theorem 1. Parallel interprocedural slicing is undecidable. It is well known that the termination problem for twocounter machines is undecidable [19]. In the remainder of this section, we reduce this problem to an interprocedural slicing problem thereby proving Theorem 1. 4.1 Two Counter Machines A two counter machine has two counter variables c0 and c1 that can be incremented, decremented, and tested against zero. It is common to use a ....

M. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

....(FPGA) for a NeuroSymbolic Processor (NSP) Some nets performing l ogical and arithmetic functions are also presented. 1. Introduction The idea of designing computers using threshold elements or neurons is as old as the McCulloch and Pitts seminal paper [4] Minsky in 1956 and later in 1967 [5,6] reported on the possibility of implementing most operations performed by a von Neumann machine using McCulloch and Pitts neurons. Minsky [6] claimed that As the control over fabrication methods improves, we can expect the more delicate threshold logic kind of circuit to play a large role. Now ....

....idea of designing computers using threshold elements or neurons is as old as the McCulloch and Pitts seminal paper [4] Minsky in 1956 and later in 1967 [5,6] reported on the possibility of implementing most operations performed by a von Neumann machine using McCulloch and Pitts neurons. Minsky [6] claimed that As the control over fabrication methods improves, we can expect the more delicate threshold logic kind of circuit to play a large role. Now the new FPGA technologies seem to provide appropriate means to fulfil these expectations. In a recent book on parallel computation by neural ....

[Article contains additional citation context not shown here]

Minsky M. L., Computation: Finite and Infinite Machines, Prentice Hall, 1967

....of computation. Unfortunately, the second, simulating the appropriate combinators has proven more difficult than expected, see Sections 5.2 and 10 for more details. 12 5.1 RAM Simulation We take machines with some fixed number n of counters as representative of random access machines. Minsky [Min67] showed that two counter RAMs are universal, but we have no hardship in allowing n 2. A RAM program is a finite sequence of instructions, numbered consecutively from 1. We assume that the last line is an end statement that appears nowhere else if two programs P; Q are concatenated, the end ....

Marvin Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

....the contents of the counters and transferring the control to the appropriate label mentioned in the instruction. The machine halts if and when the control reaches the halt instruction at label X n . We recall now the well known fact that the halting problem for Minsky machines is undecidable [20]: there is no algorithm which decides whether or not a given Minsky machine halts. Given a Minsky machine C, we define the net N C = h P; T; F; Sigma; i with initial marking M 0 as follows. ffl The set of places is P = f c 1 ; c 2 ; c m ; X 1 ; X 2 ; X n ; U g. 15 X 0 c j ....

M. Minsky, "Computation: Finite and Infinite Machines," Prentice Hall, 1967.

....show that undecidability arises even if the token takes values from a binary domain. The decidability results in this chapter hold for a token with a single value. Thus the information carrying capacity of the token defines the boundary between decidability and undecidability. A 2 counter machine [Min 62] has four types of instructions : an increment and decrement for each counter, a zero test, and a halt instruction. The halting problem for 2 counter machines is known to be undecidable. We reduce this problem to the parameterized model checking problem by using a ring of size n to simulate n ....

Minsky, M. Computation : Finite and Infinite Machines, Prentice-Hall, 1962.

....many solutions to the original problem and to some variations of it have been given. The early results all focused on the synchronization in minimal time of a linear CA. Minsky showed that a solution to the FSSP requires at least (2n Gamma 1) time, where n is the number of cells in the line [11]. Waksman in [16] gave the first solution in this minimal time, and Mazoyer in [9] constructed a minimal time solution with the least number of states to date: six (in [1] it has been shown that five states are always necessary) A significant amount of papers have also dealt with some variations ....

F. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, 1967.

....that undecidability arises even if the token takes values from a binary domain. The decidability results in this chapter hold for a token with a single value. Thus the information carrying capacity of the token defines the boundary between decidability and undecidability. A 2 counter machine [Min 62] has four types of instructions: an increment and decrement for each counter, a zero test, and a halt instruction. The halting problem for 2 counter machines is known to be undecidable. We reduce this problem to the parameterized model checking problem by using a ring of size n to simulate n ....

Minsky, M. Computation : Finite and Infinite Machines, Prentice-Hall, 1962.

....Theorem 4. Let q 1 and q 2 be event queries in the algebra E 2 where each uses one instance of either ; F or ; L . Then the problem of whether q 1 ) q 2 is undecidable. Proof. We present a proof for the LIFO consumption semantics, it is virtually identical for FIFO. Given a Minsky machine [8] (abbreviated MM and defined below) we define a set of primitive and complex events used by an event query q, which checks whether the event history is a faithful representation of the computation of the MM. q is satisfiable iff the MM terminates. It also has the property that it can be rewritten ....

....be rewritten in the form q = q 1 k q 2 and is thus satisfiable iff : q 1 ) q 2 ) Thus, we are able to define two queries q 1 and q 2 (each using one instance of LIFO) which depend on the MM specification, and q 1 ) q 2 iff the Minsky machine terminates a problem which is undecidable. An MM [8] is a sequence of n instructions S 0 : com 0 ; S 1 : com 1 ; Sn : comn where each instruction com i has one of the following forms S i : c 1 = c 1 1; goto S j S i : c 2 = c 2 1; goto S j S i : if c 1 = 0 goto S j else c 1 = c 1 Gamma 1; goto S k S i : if c 2 = 0 goto S j else c 2 ....

M. Minsky. Computation: Finite and Infinite Machines. Prentice Hall, 1967.

.... [18] Its adoption was considered necessary in order to increase the description capacity of the Petri net by allowing control structures to be modeled in which the activation of a process is a consequence of the presence of no events (i.e. ability to test for zero) It has been proved [19] [15] that a Petri net with zero testing capability produces a representation which can model any system with the computational capacity of the Turing machine. The extension resulting from the introduction of inhibitor arcs makes it possible to represent situations which could not be modeled through ....

- M. MINSKY. "Computation: finite and infinite machines". Englewood Cliffs, N.J., Prentice Hall, 1967.

..... The input of such a machine is a non negative integer n, corresponding to the initial configuration (n; 0; q 0 ) The machine halts on the input n iff there is a finite sequence of transitions yielding a configuration (n 0 ; m 0 ; q f ) with q f 2 Q f . The following problem is undecidable [Min67]: Input : a two counter machine M and a non negative integer n Question : Does M halt on n 18 We may assume without loss of generality that q 0 6= q 00 whenever Delta(q) i; q 0 ; q 00 ) if q 0 = q 00 , it suffices to introduce two new states q 0 1 and q 0 2 and let ....

Marvin L. Minsky. Computation: Finite and Infinite Machines. Prentice Hall, London, 1 edition, 1967.

....paradigms, both in theory and in practice. Hence, AI has always focused strongly on digital computation as its fundamental metaphor, to the virtual exclusion of analog computation. This preoccupation directly mirrors the situation in computer science in general, where the classic texts and reviews (Minsky 1967; Hopcroft and Ullman 1979; Lewis and Papadimitriou 1981; Hey 1999) are virtually silent on the topic of analog computation. Almost certainly, this reflects the availability of a formal, discrete state model of computation the universal Turing machine (Turing 1936; Herken 1988) which ....

Minsky, M. (1967). Computation: Finite and Infinite Machines. Englewood Cliffs, NJ: Prentice-Hall.

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Minsky, M. (1967), "Computation: Finite and Infinite Machines," Prentice Hall, New York.

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M. Minsky. Computation finite and infinite machines. Prentice-Hall, New Jersey, 1967.

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Minsky, M. L. (1967), Computation: Finite and Infinite Machines, Prentice Hall.

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M.L. Minsky. Computation: finite and infinite machines. 1967.

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Minsky, M. Computation: Finite and Infinite Machines. Prentice Hall, 1967.

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M.L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs, 1967.

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M.L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, NJ, 1967.

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Marvin Minsky. Computation: Finite and infinite machines. Prentice-Hall, London, 1972.

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Marvin Minsky. Computation: Finite and Infinite Machines, Prentice-Hall 1967.

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Marvin Minsky. Computation: Finite and Infinite Machines. Prentice-Hall 1967.

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Marvin Minsky. Computation: Finite and infinite machines. Prentice-Hall, London, 1972.

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M Minsky. Computation: Finite and Infinite Machines. Prentice--Hall, 1967.

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M. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.

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M. L. Minsky. Computation: Finite and Infinite Machines. PrenticeHall, 1971.

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M. Minsky. Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cli#s, NJ, 1967. 28

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Minsky, M., 1967, Computation: Finite and Infinite Machines, Englewood Cli#s, NJ: Prentice-Hall.

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M.L. Minsky, Computation: Finite and Infinite Machines,Prentice Hall, Englewood Cliffs, N.J., 1967.

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M.L. Minsky. Computation: finite and infinite machines. Prentice-Hall, 1967.

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Minsky, M. L. Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cli#s, N.J., 1967, Sec. 12.2--12.5, pp. 222--232.

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Marvin L. Minsky. Computation: Finite and infinite machines. Prentice-Hall, Englewood Cliffs, 1967.

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Minsky, M.L., Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, NJ (1967).

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Minsky, M. L. Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cli#s, N.J., 1967, pp. 54, 55, 66.

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] Minsky, M. L. Computation: Finite and Infinite Machines, Prentice-Hall, 1967.

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M. Minsky. Computation: Finite and Infinite Machines. PrenticeHall (1967).

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