min max game theory and nonstandard differential riccati equations for abstract hyperbolic like equations abstract we consider the abstract dynamical framework of lasiecka and triggiani 2000 1 chapter 9 which models a large variety of mixed pde problems see specific classes in the introduction with boundary or point control all defined on a smooth bounded domain r n n arbitrary this means that the input solution map is bounded on natural function spaces we then study min max game theory problem over a finite time horizon the solution is expressed in terms of a positive self adjoint time dependent riccati operator solution of a non standard differential riccati equation which expresses the optimal qualities in pointwise feedback form in concrete pde problems both control and deterministic disturbance may be applied on the boundary or as a dirac measure at a point the observation operator has some smoothing properties

evaluation of queries in independent database schemes a simple characterization of independent database schemes is proved an algorithm is given for translating a tableau t posed as a query on a representative instance to a union of tableaux that is equivalent to t but can be applied directly to database relations the algorithm may take exponential time in the size of t and the database scheme and it is applicable only to independent database schemes if t is a just a projection of a representative instance then the algorithm has a simpler form which is still exponential in the worst case and is polynomial in some cases

algorithms for computing preimages of cellular automata configurations this paper investigates pre images ancestors or past configurations of specified configurations of one dimensional cellular automata both counting and listing of pre images are discussed the main graphical tools used are the de bruijn diagram and its extension the pre image network which is created by concatenating de bruijn diagrams the counting of pre images is performed as the multiplication of topological matrices of de bruijn diagrams listing of pre images is described using two algorithms the first algorithm traces paths in the pre image network and focuses on local knowledge of the network the second performs a complete analysis of the network before proceeding with listing

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

attractor stability in nonuniform boolean networks the attractor graph of a boolean network f has the attractors of f as vertices there is a directed edge between attractors a i and a j if there is a state x a i and an index k such that x when perturbed in the kth coordinate yields a state x in the basin of attractor a j kauffman 2007 proposed to use the strongly connected components of the attractor graph called ergodic sets to model possible targets for cell differentiation however computational follow up work by him and others has revealed that most boolean networks have a single strongly connected component in an overwhelming number of cases and two strongly connected components in rare cases as a proof of concept we explicitly construct classes of hierarchical nonuniform boolean networks where the attractor graph may have an arbitrary number of ergodic sets the construction uses threshold functions and networks that are combinations of connected cliques earlier work does not address the structure of ergodic sets building on the previous construction we show how to generate boolean networks where ergodic sets possess binary hyper cubes q 2 m as sub graphs although the focus of this paper is to demonstrate that there are boolean networks with a large number of ergodic sets and that ergodic sets can be arbitrarily large we remark that networks we construct have community structure and the results may therefore be relevant to application areas ranging from biology to social science the results also provide a starting point for additional studies into the attractor structure of boolean networks their basins of attractions and conditions for stability under state noise

elements of a theory of simulation ii sequential dynamical systems we study a class of discrete dynamical systems that is motivated by the generic structure of simulations the systems consist of the following data a a finite graph y with vertex set 1 n where each vertex has a binary state b functions f i f 2 n f 2 n and c an update ordering p the functions f i update the binary state of vertex i as a function of the state of vertex i and its y neighbors and leave the states of all other vertices fixed the update ordering is a permutation of the y vertices by composing the functions f i in the order given by p one obtains the sequential dynamical system sds f y p email protected i 1nf p i f 2 n f 2 n we derive a decomposition result characterize invertible sds and study fixed points in particular we analyse how many different sds that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number finally some specific sds are investigated

answering queries on embedded complete database schemes it has been observed that for some database schemes users may have difficulties retrieving correct information even for simple queries the problem occurs when some implicit piece of information defined on some subset of a relation scheme is not explicitly represented in the database state in this situation users may be required to know how the state and the constraints interact before they can retrieve the information correctly in this paper the formal notion of embedded completeness is proposed and it is shown that schemes with this property avoid the problem described above a polynomial time algorithm is given to test whether a database scheme is independent and embedded complete under the assumption of independence it is shown that embedded complete schemes allow efficient computation of optimal relational algebra expressions equivalent to the x total projection for any set of attributes x

chandrasekhar equations for infinite dimensional systems ii unbounded input and output case abstract a set of equations known as chandrasekhar equations arising in the linear quadratic optimal control problem is considered in this paper we consider the linear time invariant systems defined in hilbert spaces involving unbounded input and output operators for a general class of such systems we derive the chandrasekhar equations and establish the existence uniqueness and regularity results of their solutions

exact controllability of the euler bernoulli equation with boundary controls for displacement and moment abstract we consider the euler bernoulli problem 1 1 in the solution w t with boundary controls g1 and g2 acting in the dirichlet traces for w and w respectively we show two main exact controllability results both in the spaces of maximal regularity of the solution at t t see i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 and both without geometrical conditions on the open bounded domain except for smoothness of its boundary one with g1 l2 0 t l2 and g2 h1 0 t l2 for any t 0 arbitrarily short and one with g1 h01 0 t l2 and g2 l2 0 t l2 for all t 0 sufficiently large an interpolation result between these two cases is also presented a direct approach is given based on two main steps first by means of an operator model i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 for problem 1 1 and a functional analytic approach the question of exact controllability is shown to be equivalent to an a priori inequality for the corresponding homogeneous problem next this a priori inequality is proved to hold true by means of multiplier techniques these are inspired by recent progress on the maximal regularity exact controllability and uniform stabilization questions for second order hyperbolic equations

inferring local transition functions of discrete dynamical systems from observations of system behavior abstract we consider the problem of inferring the local transition functions of discrete dynamical systems from observed behavior our focus is on synchronous systems whose local transition functions are threshold functions we assume that the topology of the system is known and that the goal is to infer a threshold value for each node so that the system produces the observed behavior we show that some of these inference problems are efficiently solvable while others are np complete even when the underlying graph of the dynamical system is a simple path we identify a fixed parameter tractable problem in this context we also consider constrained versions of threshold inference problems where the input includes a set of equality or inequality constraints which specify pairs of nodes which must have the same threshold value or different threshold values we present algorithmic and complexity results for several constrained threshold inference problems

riccati equations for hyperbolic partial differential equations with l 2 0 t l 2 γ dirichlet boundary terms this paper studies the quadratic optimal control problem for second order linear hyperbolic partial differential equations defined on a bounded domain omega subset r n with boundary gamma both the finite interval case 0 t t infty and the infinite interval case t infty regulator problem are considered the distinguishing feature of the paper which differentiates it from previous scarce literature on the subject is that the controls are only l 2 0 t l 2 gamma functions which act in the dirichlet b c and that the corresponding solutions are penalized in the l 2 0 t l 2 omega norm smoother controls particularly in space were taken in the few previous works on this subject the well posedness of this formulation stems from recent results by the authors about regularity of second order hyperbolic mixed problems l t 1 l t 3 under minimal assumptions the optimal control is synthesized in a pointwise feedback form through an operator which is s

modeling and analyzing social network dynamics using stochastic discrete graphical dynamical systems motivated by applications such as the spread of epidemics and the propagation of influence in social networks we propose a formal model for analyzing the dynamics of such networks our model is a stochastic version of discrete graphical dynamical systems using this model we formulate and study the computational complexity of two fundamental problems called reachability and predecessor existence problems which arise in the context of social networks we also address other problems that deal with the time evolution of such stochastic dynamical systems further we point out the implications of our results to problems for other computational models such as hopfield networks communicating finite state machines and systolic arrays in particular our polynomial time algorithms for the predecessor existence problem for stochastic dynamical systems imply similar results for one dimensional finite cellular automata

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author the main goal is to provide a tutorial of ca theory to researchers in other branches of natural computing to give a compact collection of known results with references to their proofs and to suggest some open problems

approximation of discrete time lqg compensators for distributed systems with boundary input and unbounded measurement abstract we consider the approximation of optimal discrete time linear quadratic gaussian lqg compensators for distributed parameter control systems with boundary input and unbounded measurement our approach applies to problems that can be formulated in a state space on which both the discrete time input and output operators are continuous approximating compensators are obtained via application of the lqg theory and associated approximation results for infinite dimensional discrete time control systems with bounded input and output numerical results for spline and modal approximation schemes used to compute optimal compensators for a one dimensional heat equation with either neumann or dirichlet boundary control and pointwise measurement of temperature are presented and discussed

predecessor existence problems for finite discrete dynamical systems we study the predecessor existence problem for finite discrete dynamical systems given a finite discrete dynamical system s and a configuration c the predecessor existence or pre problem is to determine whether there is a configuration c such that s has a transition from c to c in addition to the decision version we also study the following variants the predecessor existence or pre problem counting the number of predecessors the unique predecessor existence or upre problem deciding whether there is a unique predecessor and the ambiguous predecessor existence or apre problem given a configuration c and a predecessor c of c deciding whether there is a different predecessor c of c general techniques are presented for simultaneously characterizing the computational complexity of the pre problem and its three variants our hardness results are based on the concept of simultaneous reductions single transformations that can be used to simultaneously prove the hardness of the different variants of the pre problem for their respective complexity classes our easiness results are based on dynamic programming and they extend the previous results on pre problem for one dimensional cellular automata the hardness results together with the easiness results provide a tight separation between easy and hard instances further the results imply similar bounds for other classes of finite discrete dynamical systems including discrete hopfield and recurrent neural networks concurrent state machines systolic networks and one and two dimensional cellular automata our results extend the earlier results of green sutner and orponen on the complexity of the predecessor existence problem and its variants

uniform exponential energy decay of wave equations in a bounded region with l2 0 l2 γ feedback control in the dirichlet boundary conditions etant donne un ouvert borne r n n 2 on considere l equation d onde w tt w dans o avec des conditions initiales w o x w o x l 2 w 1 o x w 1 x h 1 et des conditions aux limites non homogenes de type dirichlet w t u t sur o etant la frontiere de

on the existence of cook semantics in siam j comput 7 1978 pp 70 90 cook defines the operational semantics of a programming language in the following way a function is introduced which takes a program r and a state sigma and yields a possibly infinite row of intermediate states as a result this row is meant to be the trace resulting from executing program r starting in state sigma this function is characterized by a number of equations however it is not immediately clear whether these equations have a solution in this paper we show for a simple language the most sophisticated feature of which is that it has parameterless procedures that the corresponding equations have a unique solution the techniques used here can also be applied to other languages described in the same way for instance to the language in cook s paper

the complexity of planar counting problems we prove the p hardness of the counting problems associated with various satisfiability graph and combinatorial problems when restricted to planar instances these problems include 3sat 1 3sat 1 ex3sat minimum vertex cover minimum dominating set minimum feedback vertex set x3c partition into triangles and clique cover we also prove the np completeness of the ambiguous satisfiability problems j b saxe two papers on graph embedding problems tech report cmu cs 80 102 dept of computer science carnegie mellon univ pittsburgh pa 1980 and the dp completeness with respect to random polynomial reducibility of the unique satisfiability problems l g valiant and v v vazirani np is as easy as detecting unique solutions in proc 17th acm symp on theory of computing 1985 pp 458 463 associated with several of the above problems when restricted to planar instances previously very few p hardness results no sf np hardness results and no dp completeness results were known for counting problems ambiguous satisfiability problems and unique satisfiability problems respectively when restricted to planar instances assuming sf p neq np one corollary of the above results is that there are no epsilon approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers

elements of a theory of simulation iii equivalence of sds in the development of mathematical foundations for a theory of simulation a certain class of discrete sequential dynamical systems sds is of particular importance these systems which we refer to as sds consist of a a graph y with vertex set 1 2 n where each vertex has associated a binary state b a vertex labeled set of functions f i y f 2 n f 2 n and c a permutation p s n the function f i y update the state of vertex i as a function of the states of vertex i and its y neighbors and leaves all other states invariant by composing these functions in the order given by p we obtain the sds f y p i 1 nf p i y f 2 n f 2 n in this paper we give a combinatorial upper bound for the number of non equivalent sds for a given graph and we compute this bound explicitly for certain classes of graphs we give a full characterization of invertible sds and analyze the set of fixed points of sequential and parallel cellular automata further we introduce the concept of maj type sds and show that systems of this class only have fixed points as attractors finally we analyze sds that are fixed point free for arbitrary base graphs

global existence for an abstract riccati initial value problem with possibly unbounded coefficients abstract we consider operator valued riccati initial value problems of the form r t tr t r t t ta t tb t r t r t tc t r t td t r t r 0 r 0 here a t through d t and r 0 have values as nonnegative bounded linear operators in l 1 where is a finite measure and t is a closed nonnegative operator in l 1 satisfying additional technical conditions for such problems the notion of strongly mild solutions is defined the main result is a set of conditions under which with sufficiently small initial value has a global solution

elements of a theory of computer simulation i sequential ca over random graphs this paper is a first step in the development of mathematical foundations for a theory of simulation we employ sequentially updated cellular automata sca over arbitrary graphs as a paradigmatic framework in the development of the theory we focus on the properties of causal dependencies among local mappings in a simulation let y be a graph in which a each vertex i has a state x i0 1 and b there exists a local map i defined on the states of the y neighbors and x i that returns the state of y i0 1 suppose i 1 i n is a permutation of the y vertices then the order of application of the local maps i k induces a sequential or asynchronous cellular automaton sca over y in this paper we introduce a mapping between the base graph y over which the sca is defined and which represents the mutual dependencies of the local maps and the update graph u y whose vertices are permutations of all y vertices two permutations p 1 p 2 are adjacent in u y if they differ in exactly two consecutive coordinates i k i k 1 and i k i k 1 ey u y represents a conceptual framework which allows to determine equivalence classes of sca for a given graph x independent of the family of local maps i 1 i n we consider a u as a random variable over g n p and analyze the induced random graph u g n p the update graph and show b that u exhibits properties of a covariant functor