Seminar on Current Trends in Theory and Practice of Informatics), Lecture Notes in Computer Science, volume 1012, pages 236--271. Springer, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of cellular automata called on line tessellation automata [13] and to the class of picture languages definable by existential expressions in monadic second order logic [9] A survey of the topic is given in the Handbook of Formal Languages [8] In the string language theory, it is well known [4, 14, 15, 19] that any recognizable string language can be obtained by projection of the intersection of the star of two finite languages. Formally, if a string language R over Sigma is recognizable, This work was partially supported by PRC GDR AMI Mod eles et Outils pour les SYst emes ....

M. Latteux and J. Leguy. On composition of morphisms and inverse morphisms. Lecture Notes in Computer Science, 154:420--432, 1983.

....of cardinality ve. OK5 is binary and mni. It follows that b(OK5 ) is binary and mni. Conjecture 6.9 (Seymour [57] A binary clutter is ideal if and only if it contains no F 7 , OK 5 or b(OK 5 ) minor. 6. 2 Binary Matroids In the remainder of this section, we present results of Novick Seb o [43] and Cornu ejolsGuenin [11] on ideal binary clutters. We adopt a matroidal point of view. See Oxley s excellent textbook [46] on matroid theory for background material. A matroid is binary if it can be represented over GF (2) Example 6.10 The Fano matroid F 7 has the following binary ....

....matroid is uniquely determined by the set of circuits containing any xed element. In particular, N and N 0 are uniquely determined by the circuits containing t. This implies N = N 0 . Since M = N=t and M 0 = N 0 =t, it follows that M = M 0 = u(H) 2 Proposition 6. 17 (Novick and Seb o [43]) A binary clutter H is the odd cycle clutter of a signed graph if and only if u(H) is a graphic matroid. A binary clutter H is the T cut clutter of a graft if and only if u(H) is a cographic matroid. 30 The next result relates the minors of the matroid u(H) to the minors of the clutter H. ....

B. Novick and A. Sebo, On Combinatorial Properties of Binary Spaces, Integer Programming and Combinatorial Optimization, E. Balas and J. Clausen eds., Lecture Notes in Computer Science 920 (1995) 212-227.

....Property 2. fs(p i )g and ft(p i )g are monotonically increasing sequences, and fh(p i )g is a monotonically decreasing sequence. Property 3. A path p i 2 Pu;v is optimal for sessions whose duration 2 [t(p i 1) t(p i ) The proposed on line algorithm uses the doubling technique, see e.g. [27]. During a session, the algorithm may reroute the session s VC so as to reduce the total cost of the session. The algorithm is iterative. An iteration starts when the algorithm determines a new route for the session s VC. This is determined using two principles: the credit principle and the ....

Y. Azar. On-line load balancing. Chapter 8 in \Online Algorithms, State of the Art", Edited by A. Fiat and G. J. Woeginger, Lecture Notes in Computer Science, Vol. 1442, Springer-Verlag, 1998.

.... The seat reservation problem is closely related to the problem of optical routing with a number of wavelengths [1, 5, 9, 14] call control [2] interval graph coloring [12] and interval scheduling [13] The o line version of the seat reservation problem can be used to solve the following problems [8]: minimizing spill in local register allocation, job scheduling with start and end times, and routing of two point nets in VLSI design. Another application of the on line version of the problem could be to assign vacation bungalows (mentioned in [15] The performance of an on line algorithm A is ....

M. C. Carlisle and E. L. Lloyd, On the k-Coloring of Intervals, Advances in Computing and Information, Lecture Notes in Computer Science 497: 90-101, Springer-Verlag, 1991.

....rewriting algebraic expressions) a more uniform format for writing solutions is sometimes used. Within the Computer Science community, a calculational paradigm for manipulating mathematical expressions has emerged. It has been attributed to W. Feijen, and it is described in detail by van Gasteren [5]. The following 1 We use the term High School here for the Finnish lukio gymnasium , i.e. years 10 12 which follow Secondary School and which prepare students for University level studies. 1 is an example of this, deriving a distribution property for set operators: v 2 A (B [ C) j fset ....

A.J.M. van Gasteren. On the Shape of Mathematical Arguments. Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1990.

....written about their usefulness in obtaining unambiguous specifications and in the verification of software properties [Kel95, Kel97, Rus95] However, the industrial take up of formal methods can be described at its best as poor. Formal methods have been used with success in hardware development [Hei98] but in software development they have been used rarely, their use being restricted mainly to safety critical software. Many reasons have been suggested for this in the literature [Sai96, Hal90a, Hoa96, Str89, Rus93] some of the most common being: 1. Problems finding the right level of ....

C. Heitmeyer. On the need for "practical" formal methods. Lecture Notes in Computer Science, 1486:18--27, 1998.

....provable rule of inference is admissible. None of the converse implications holds in a general case. It is important to notice that there are serious reasons to assume that derivable and provable rules alone are not sucient for an advanced system of automated deduction and veri cation (cf. also [14]) Example 1. Here are examples of widely used admissible rules that are not provable: 8x (generalization) x) y) renaming of free variables) where is a 1 sentence (Markov rule for intuitionistic arithmetic HA, cf. 17] disjunctive and existential rules for intuitionistic ....

....variables, formalization, L ob rule and internally veri able. The rules implicit re ection, Markov rule, disjunctive rule, existential rule are not internally veri able. We accept the understanding of stability as conservativity of extensions by internally veri able rules (cf. 1] 8] 11] [14]) De nition 7. System V 0 V is conservative over V if for any formula V 0 implies V : A system V is stable if for any rule = veri able in V the system V = is conservative over V. De nition 8. By IRR(V) we denote the implicit re ection rule = where represents the ....

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Pollack, R.: On Extensibility of Proof Checkers. Lecture Notes in Computer Science, Vol. 996. Springer-Verlag, Berlin Heidelberg New York (1995) 140-161

.... The seat reservation problem is closely related to the problem of optical routing with a number of wavelengths [1, 5, 9, 14] call control [2] interval graph coloring [12] and interval scheduling [13] The o line version of the seat reservation problem can be used to solve the following problems [8]: minimizing spill in local register allocation, job scheduling with start and end times, and routing of two point nets in VLSI design. Another application 2 of the on line version of the problem could be to assign vacation bungalows (mentioned in [15] The performance of an on line algorithm A ....

M. C. Carlisle and E. L. Lloyd, On the k-Coloring of Intervals, Advances in Computing and Information, Lecture Notes in Computer Science 497: 90-101, Springer-Verlag, 1991.

....this is believed to be the case, for related results see [18] In contrast, Yannakakis [19] proved that in communication complexity this 4 restriction is as severe as can be, namely, that P cc = UP cc . The somewhat less restrictive class FewP was introduced by Allender [1] and studied in [5, 6]. As it contains UP , it is at least as hard. A corollary to our main result (Corollary 1) is a strengthening of the result of Yannakakis above, namely we prove P cc = FewP cc (where in FewP cc we allow each input to have polylogarithmic number of witnesses, as well as total polylog number ....

J. Cai, L.A. Hemachandra, On the power of parity, Proc. of the 6th STACS, Lecture Notes in computer science, Vol 349 (1989), 229--240, Springer Verlag.

....mean response time is shortest remaining processing time rst (SRPT) In addition to SRPT, there are many algorithms in the literature which are designed for the case where the task size is known. Good overviews of the single node scheduling problem and its solution are given in [7] 14] and [17]. In our work we focus on servers that serve static content, i.e. les whose size can be determined in advance. Web servers can serve dynamic content as well; in this case our methods are less directly applicable. However, recent measurements have suggested that most servers serve mainly static ....

M. Pinedo. On-line algorithms, Lecture Notes in Computer Science. Prentice Hall, 1995.

....time machines, and show results that exploit the fact that the machines for these classes have a bounded number of accepting computation paths. We will not only consider these subclasses of NP, namely UP and FewP, but also the class Few, an extension of FewP defined by Cai and Hemachandra [CaHe89], in which the accepting mechanism of the machine is more flexible. 1 The three classes UP, FewP and Few are all defined in terms of nondeterministic machines with a bounded number of accepting paths for every input string, but for the last two classes this number is not known beforehand, and ....

....language L in the mentioned classes a polynomial time nondeterministic machine can be constructed that has exactly f(x) 1 accepting paths for strings x in L, and f(x) accepting paths for strings x that are not in L where f is a polynomial time computable function. This fact extends a result in [CaHe89], where it was proved that the classes FewP and Few are included in PhiP. From our result follows additionally that FewP and Few are contained in the counting class C = P (exact counting) Wa86] thus answering a question proposed in [Sc88] We use the above result to prove in Section 4 ....

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J. Cai and L.A. Hemachandra. On the power of parity. Symp. Theor. Aspects of Comput. Sci., Lecture Notes in Computer Science, Springer-Verlag, (1989), 229--240.

....A particular instance of the box algebra is PBC (Petri Box Calculus) 3, 4] whose development was a direct inspiration for the introduction of the box algebra. The technique of associating a Petri net with a process algebra expressions has also been studied for various other process algebras [10, 13, 17, 18, 25, 28]. The box algebra is parameterised by a set of operators, OpBox, which can be used to construct valid box expressions. For each operator op 2 OpBox, there is an associated operator in the domain of boxes, Omega op . This allows one to compositionally define, for every composite box expression E ....

U. Goltz: On Representing CCS Programs by Finite Petri Nets. Proc. of MFCS'88, M. P. Chytil, L. Janiga and V. Koubek (Eds.). Springer-Verlag, Lecture Notes in Computer Science 324 (1988) 339-350.

....Assume F is a folding architecture with N neurons and W weights. If the activation function is H then VC(F h ) O(NWk Wh log k W log W ) if k 2 O(NW W log(hW ) if k = 1 : If the activation function is sgd then PS(F h ) 2h ) if k 2 ) if k = 1 : Additionally, from [KS2, H1] the lower bounds follow: VC(F h ) Omega Gamma W log(Wh) if oe = H and PS(F h ) Omega Gamma Wh) if oe = sgd. In the case of the Heavyside function one can improve the lower bound for k 2: Theorem 11 If oe = H and k 2 then VC(F h ) Omega Gamma Wh W log W ) 15 according to the ....

.... a condition different to the entropy condition is useful in practise, i.e. with the assumption of noise [V] The class of folding networks has infinite VC or pseudodimension, the same is valid for the scale sensitive version of the pseudodimension even in the case of limited weights and inputs [H1]. It is an interesting question whether this is due to the function class or a characteristic of the input set and its recursive structure. Do interesting function classes exist on trees with finite VC dimensions One function class to consider in this context is folding networks with activation H ....

B. Hammer, On the generalization of Elman networks, 7th International Conference on Artificial Neural Networks, 1997, W. Gerstner et.al. (eds.), Lecture Notes in Computer Science, Springer, Berlin, 409414.

....random tilings, and how to calculate the number of local moves or ips required to transform one tiling into another. We also analyze the lattice structure of the set of tilings, and study several examples with three and four colors as well. 1 Introduction Tilings of the plane with Wang tiles [1, 8] have been studied in computer science since the famous result of Berger [4] that the problem of whether we can tile the in nite plane using a given set of Wang tiles is undecidable. This paper focuses on tilings of a given nite region with colored boundary. This is a well known NP complete ....

K. Culik and J. Kari, \On Aperiodic Sets of Wang Tiles." Lecture Notes in Computer Science 1337 (1997) 153-162.

.... of each logic in the hierarchy consists of a formula of a certain fragment of transitive closure logic pre xed with an existentially quanti ed tuple of unary relation symbols (which can appear in the formula ) In essence, it is the hierarchy of transitive closure logic studied by Gr adel in [7] (and shown there to be proper on the class of all nite structures) but with formulae pre xed with existentially quanti ed tuples of unary relation symbols. The question we will mainly be concerned with is: Is the hierarchy still proper even when we allow pre xes of existentially quanti ed unary ....

.... coloured structure is the expansion of A by the chosen relations X 1 ; X 2 ; X q (and so it is a [ hX 1 ; X 2 ; X q i structure) 3 Our Ehrenfeucht Fra ss e game Our Ehrenfeucht Fra ss e game is a natural amalgamation of the Ajtai Fagin game from [1] and the Gr adel game from [7]. De nition 1 Let be some signature and let be some problem over . The mon 1 1 TC game for is played between Spoiler and Duplicator, and proceeds in the following way. Spoiler chooses some positive integer k and a number s of sets. He then fetches k pairs of pebbles (p 1 ; q 1 ) p ....

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E. Gradel, On transitive closure logic, Lecture Notes in Computer Science 626, Springer-Verlag (1991) 149-163.

....presentation. First we introduce the the language with constants LK , and then we present again the language with replication L ( For the language with constants, we give two different transition semantics. First we present early transition rules R IDE , slightly modified from those used in [12]. Next we present similar early transition rules RUNW with an unwinding rule. Finally, we present early transition rules for the processes defined in L ( The first bisimulation relates process P considered with R IDE , to process P considered with RUNW . The second bisimulation relates ....

....fact that j . 2 5 A brief interlude: constants versus replication. 48 Hence we have shown that C . This is sufficient to conclude that C . Hence Q and ( k) b Q j E) are strongly bisimilar. 6 An example: the spanning tree program. We take our example from Philippou and Walker s paper [12]. The calculus presented in this paper is slightly different from that in section 5; it has for rule 1 x( y) P xh zi Gamma Pf z= yg (the sorts of the components of y and z agree) which differs from our rule 1, only in the side condition. However, since the example program we are ....

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A. Philippou and D. Walker, On Confluence in the -calculus. Lecture Notes in Computer Science, 1256:314--324, Springer-Verlag, 1997.

....no more than the number of cyclic faces in the planar embedding of the graph minus 1. Cai, Deng, and Zang [10] obtained a 2. 5 approximation algorithm for the minimum feedback vertex set problem on tournaments, improving the previously known algorithm with performance guarantee of 3 by Speckenmeyer [84]. Let H be the triangle vertex incidence matrix of a tournament T and let e be the all one vector. In [10] necessary and sufficient conditions are established for the linear system x Hx # e, x # 0 to be a totally dual integral system (TDI) Definition 1. A rational linear system x ....

E. Speckenmeyer: 'On feedback problems in digraphs', Lecture Notes in Computer Science, Springer-Verlag Vol.411 (1989), 218-231.

....and with this mapping we construct another mapping of jets of order k to jets of order k 1. And we prove this mapping generalizes the formal derivation. The advantage for this approch is we use the topological methods and it s possible to obtains the set of formal solution in certains case [25] 2. Space of Ehresmann We recall the jet space of Ehresmann (inspired by [4] Let x 2 R n , u 2 R m and consider a germ of C 1 functions : f : R n Gamma Gamma Gamma R m verifying f(x) u. On the This work is supported by the DFG grant Ca 153 4 1 2 Jirung Albert SHIH set of ....

J.A.Shih On the Determination of Formal Solutions of a System of PartialDifferential Equations, Lecture Notes in Computer Science 948, Springer Verlag.

....derivation rules [23] A particular instance of the box algebra is the Petri Box Calculus (PBC) 3, 4, 11, 15] a direct inspiration for the introduction of the box algebra. Note that the technique of associating Petri nets with process algebra expressions has also been studied for other models [9, 10, 13, 14, 22, 25]. The model we are going to describe is based on a set of operators, OpBox, which can be used to construct valid box expressions. For each operator op 2 OpBox there is an associated operator in the domain of boxes, Omega op . This allows one to compositionally define, for every box expression E = ....

....in a choice with N ff , yielding the net shown on the right hand side of figure 6. This net, however, allows evolutions such as ffigffigfffg, which do not correspond to what one expects from a choice construct. This phenomenon is not particular to our approach, nor to Petri nets in general (cf. [1, 13]) If we imposed ex directedness on all boxes, then the problem would disappear. However, such a strict solution is not always desirable, because boxes such as Omega are useful in modelling guarded whileloops in programming languages (basically, v 1 corresponds to the negation of the guard(s) ....

U. Goltz: On Representing CCS Programs by Finite Petri Nets. Proc. of MFCS'88, M. P. Chytil, L. Janiga and V. Koubek (Eds.). Springer-Verlag, Lecture Notes in Computer Science 324 (1988) 339-350.

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Kokosi'nski Z.: On parallel generation of t--ary trees in an associative model. PPAM 2001, Lecture Notes in Computer Science 2328 (2002) 228--235

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J. Dj. Goli#c. On the security of nonlinear #lter generators. Fast Software Encryption, Lecture Notes in Computer Science, vol. 1039, D. Gollmann ed., Springer, pages 173#188, 1995.

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Larry Bull. On ZCS in Multi-agent Environments. Lecture Notes in Computer Science, 1498:471-480, 1998.

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Workshop on Tools and Algorithms for the Construction and Analysis of Systems #TACAS#, Lecture Notes in Computer Science. Springer-Verlag, 1998.

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Workshop on Computer Aided Verification, CAV89, Grenoble, June 1989. Lecture Notes in Computer Science, Springer-Verlag.

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