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1.
The minimal number(S) of generators of a multidimensional systemS is constructively determined. Such anS is the solution space of a linear system of partial differential or difference equations with constant coefficients. The main theorem generalizes recent results of Heij and Zampieri who calculated the number(S) in the one- (resp. two-) dimensional discrete case. There is also a direct connection with Macaulay's inverse systems in the multidimensional discrete situation, in particular with his principal systems characterized by the relation(S)1. It is surprising that, for dimensions greater than one, very many large systems are principal in this sense.  相似文献   

2.
In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.  相似文献   

3.
A process is calledcomputable if it can be modelled by a transition system that has a recursive structure—implying finite branching. The equivalence relation between transition systems considered is strong bisimulation equivalence. The transition systems studied in this paper can be associated to processes specified in common specification languages such as CCS, LOTOS, ACP and PSF. As a means for defining transition systems up to bisimulation equivalence, the specification languageCRL is used. Two simple fragments of,CRL are singled out, yielding universal expressivity with respect to recursive and primitive recursive transition systems. For both these domains the following properties are classified in the arithmetical hierarchy:bisimilarity, perpetuity (both 1 0 ),regularity (having a bisimilar, finite representation, 2 0 ),acyclic regularity ( 1 0 ), anddeadlock freedom (distinguishing deadlock from successful termination, 1 0 ). Finally, it is shown that in the domain of primitive recursive transition systems over a fixed, finite label set, a genuine hierarchy in bisimilarity can be defined by the complexity of the witnessing relations, which extends r.e. bisimilarity. Hence, primitive recursive transition systems already form an interesting class.  相似文献   

4.
A representative system defined onn voters or propositionsi = 1,,n is a functionF: {1,0, -1} n {1,0, -1} which is monotonic (D E F(D) F(E)), unanimous (F(1,, 1) = 1), dual (F(-D) = -F(D)), and satisfies a positivity property which says that the set of all non-zero vectors in {1, 0, -1} n for whichF(D) = 0 can be partitioned into two dual subsets each of which has the property that ifD andE are in the subset thenD i+E i > 0 for somei. Representative systems can be defined recursively from the coordinate projectionsS i (D) = D i using sign functions, and in this format they are interpreted as hierarchical voting systems in which outcomes of votes in lower levels act as votes in higher levels of the system. For each positive integern, (n) is defined as the smallest positive integer such that all representative systems defined on {1, 0, -1} n can be characterized by(n) or fewer hierarchical levels. The function is nondecreasing inn, unbounded above, and satisfies(n) n–1 for alln. In addition,(n) = n–1 forn {1, 2, 3, 4}, and it is conjectured that does not continue to grow linearly asn increases.  相似文献   

5.
A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ) = h(t, x(t; )) + s k(t, s; )f(s, x(s; ); )d(s) is studied wheret S, a measure space with certain properties, , the supporting set of a probability measure space (,A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be an almost surely continuousm-dimensional vector-valued stochastic process onS which is bounded with probability one for eacht S and which satisfies the equation almost surely. Several theorems are proved which give conditions such that a unique random solution exists. AMS (MOS) subject classifications (1970): Primary; 60H20, 45G99. Secondary: 60G99.  相似文献   

6.
The necessary conditions obtained by the author in a previous study for the extremum of a functional that depends on the control function on the compact set and on a -measurable subset in (where is the ordinary Lebesgue measure) subject to functional equality and inequality constraints are generalized here to an arbitrary continuous Radon measure.Translated from Kibernetika, No. 4, pp. 69–73, July–August, 1990.  相似文献   

7.
O. Hájek proved in his book Dynamical Systems in the Plane (Chapter III) that there isat most one abstract local dynamical system which is locally equivalent to, or equivalently an extension of, a given elementary dynamical system, and suggested a question of finding reasonable conditions on the latter for the existence ofat least one such abstract local dynamical system. An elementary dynamical system is said to satisfy the No-Intersection Axiom and is called an abstract germ if(x 1, t) = (x 2,t) impliesx 1 =x 2. We show that is (uniquely) extendable to an abstract local dynamical system if and only if is an abstract germ, and hence the question is completely answered. After introducing various kinds of isomorphisms of abstract germs and abstract local dynamical systems corresponding to those of continuous germs and continuous local dynamical systems, we obtain some sufficient conditions for extendability of isomorphisms and possibility of restriction of them, and thus establish the local determinacy of abstract local dynamical systems up to isomorphisms in some wider categories.Dedicated to Professor Yusuke HAGIHARA in Commemoration of His Seventy-Seventh Anniversary  相似文献   

8.
We describe the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity: for distinct odd primes p and q, the congruences x 2 q (mod p) and x 2 p (mod q) are either both solvable or both unsolvable, unless pq3 (mod 4). The proof is a formalization of an argument due to Eisenstein, based on a lemma of Gauss. The input to the theorem prover consists of nine function definitions, thirty conjectures, and various hints for proving them. The proofs are derived from a library of lemmas that includes Fermat's Theorem and the Gauss Lemma.  相似文献   

9.
Property preserving abstractions for the verification of concurrent systems   总被引:9,自引:0,他引:9  
We study property preserving transformations for reactive systems. The main idea is the use of simulations parameterized by Galois connections (, ), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function mapping sets of states of a systemS into sets of states of a systemS'. We give results on the preservation of properties expressed in sublanguages of the branching time -calculus when two systemsS andS' are related via (, )-simulations. They can be used to verify a property for a system by verifying the same property on a simpler system which is an abstraction of it. We show also under which conditions abstraction of concurrent systems can be computed from the abstraction of their components. This allows a compositional application of the proposed verification method.This is a revised version of the papers [2] and [16]; the results are fully developed in [28].This work was partially supported by ESPRIT Basic Research Action REACT.Verimag is a joint laboratory of CNRS, Institut National Polytechnique de Grenoble, Université J. Fourier and Verilog SA associated with IMAG.  相似文献   

10.
Thermal bubble powered micro mechanical actuators have been successfully demonstrated in working liquids. Micro mechanical plates which function as the mechanical actuators are 70×60×2 m3 in size. They have been fabricated by surface-micromachining technology and suspended 2 m above the substrate by the supports of cantilever beams. Micro thermal bubbles which are generated by heavily phosphorus doped polysilicon line resistive heaters have been used to lift the mechanical plates in a controllable manner. The typical current required to generate a single, spherical thermal bubble as the actuation source on top of the micro line resistors (60×2×0.3 m3 in size) is 8.4 mA (80 m Watt) in FC 43 liquid (an inert, dielectrical fluid available from the 3M company). The thermal bubbles have been demonstrated to actuate the mechanical plate perpendicularly to the substrate with a maximum elevation distance of 140 m and a maximum actuation force of 2 N. This new actuation mechanism is expected to find applications for micro fluidic devices.The authors would like to thank Prof. V.P. Carey, Mechanical Engineering department, U.C. Berkeley and Dr. A.P. Lee for valuable discussions. The devices were fabricated in the UC Berkeley Microfabrication Laboratory and the FC liquid was provided by 3M company. This work has been supported by Berkeley Sensor and Actuator Center, an NSF/Industry/University Co-operative Research Center.  相似文献   

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