efficient parallel rooting of complex polynomials on the unit circle an efficient method is presented for rooting complex polynomial equations of any order where the root space is restricted to the unit circle the method restates the evaluation of polynomials as a recursive algorithm involving only additions by means of the bilinear transformation the straight line uniformly spaced recursive polynomials evaluation method of a h nuttall 1987 is extended to the unit circle where the root positions are determined by thresholding general coefficient transformations are provided along with a comparison to the horner method

countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps abstract in this work we investigate stochastic partial differential equations with variable delays and jumps we derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions and generalize the results obtained by taniguchi t taniguchi the exponential stability for stochastic delay partial differential equations j math anal appl 331 2007 191 205 and wan and duan l wan j duan exponential stability of non autonomous stochastic partial differential equations with finite memory statist probab lett 78 5 2008 490 498 to cover a class of more general stochastic partial differential equations with jumps finally an illustrative example is established to demonstrate our established theory

a topological property of rational w languages abstract we prove that any rational subset k of a is the set of cluster points of a equipped with some ultrametric distance having some specific properties

estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

strong fairness and ultra metrics abstract we answer an open question of costa and hennessy and present a characterization of the infinite fair computations in finite labeled transition systems without any structure of the states as cluster points in metric spaces this technique is applied to reduce the logical complexity of several known fairness concepts from 03 to 02 and from 11 to 03 respectively

efficient evaluation of 1 d and 2 d polynomials at equispaced points an extension to the two dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two dimensional polynomials efficiently over general periodic parallelograms the problem of getting the initial values required for other fast algorithms is treated in a general manner fast algorithms are presented for computing initial values in both cases of one and two dimensional polynomials it is observed that the two dimensional recursion is not always advantageous compared with taking the one dimensional recursion for each variable separately

analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients this paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations psdes two criteria are proposed to guarantee exponential stability of the solution the first criterion is a khasminskii type condition involving general lyapunov functions the second is developed on coefficients of the equation in virtue of m matrix techniques based on the second criterion robust stability of a perturbed hybrid psde is also investigated the theory shows how much an exponentially stable hybrid psde can tolerate to remain stable

neutral stochastic functional differential equations with infinite delay and poisson jumps in the cg space abstract in this paper we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay and poisson jumps insfdeps in short in the phase space c g with non lipschitz coefficients furthermore we study the continuous dependence of the solution on the initial value by means of the corollary of the bihari inequality

asymptotic stability in the pth moment for stochastic differential equations with levy noise abstract this paper is devoted to study a class of stochastic differential equations with levy noise in comparison to the standard gaussian noise levy noise is more versatile and interesting with a wider range of applications however levy noise makes the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty we propose several sufficient conditions under which we investigate the long time behavior of the solution including the asymptotic stability in the pth moment and almost sure stability also we discuss two types of continuity of the solution continuous in probability and continuous in the pth moment finally we provide two examples to illustrate the effectiveness of the theoretical results

on fast evaluation of bivariate polynomials at equispaced arguments the initial value problem arising in the recursive evaluation of a 2d polynomial at equispaced points is treated in detail the results facilitate efficient implementation of bose s recursive algorithm the computational complexity is compared with that involved in a direct computation and some general observations are made for an alternative scheme proposed by x nie and r unbehauen 1989

on the solvability of domino snake problems abstract in this paper we present an extensive treatment of tile connectability problems sometimes called domino snake problems the interest in such problems stems from their relationship to classical tiling problems which have been established as an important simple and useful tool for obtaining basic lower bound results in complexity and computability theory we concentrate on the following two contrasting results the general snake problem is undecidable in a half plane due to ebbinghaus but is decidable in the whole plane this surprising decidability result was announced without proof by myers in 1979 we provide here the first full proof and show that the problem is actually pspace complete we also prove many results concerning the difficulty of variants of these general snake problems and their extension to infinite snakes in addition we establish a resemblance between snake problems and classical tiling problems considering the corresponding bounded unbounded and recurring cases

finite limiting effects for a band limited gaussian random process with applications to a d conversion the theory of finite limiting effects for a bandlimited gaussian random process is reviewed and a mathematical expression for the asymptotic distortion spectrum is derived which is accurate for frequencies outside of the original bandwidth an expression is also derived for the total distortion power which is shown to be useful for estimating the aliased distortion spectrum when sampling is used to form a discrete time signal combining these results with the asymptotic distortion spectrum also gives an estimate of the dc power of the distortion an important application of these results is in a d analog to digital conversion where the input signal is implicitly limited by the largest quantization level curves are given for the overall signal to distortion plus quantization noise ratio sdqr as a function of normalized input level and number of bits carried the maximum sdqr is realized over a narrow range of input levels which is centered at about 12 dbfs relative to full scale for an 8 bit a d

a high resolution data adaptive time frequency representation a data adaptive time frequency representation is developed that overcomes some limitations of the short time fourier transform while avoiding the cross terms that make the wigner distribution and other bilinear representations difficult to interpret the adaptive time frequency representations uses gaussian basis functions but varies their time width and chirp rate with time and frequency to achieve high signal concentration everywhere a measure of local signal concentration allows fully automated determination of the optimal basis parameters the adaptive method is computationally expensive but may provide much better performance than any currently known technique

undecidability principle and the uncertainty principle even for classical systems it is shown that for any physical system there is an infinite number of measurements which are related to one of the undecidable problems the undecidability of the physical systems indicates that there is an infinite number of incomputable correlation functions for each physical system these results show that there is an inherent and irreducible limitation on the knowledge of the nature of physical systems this uncertainty principle is caused by the undecidability principle

efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments a kth order polynomial can be evaluated by means of k additions and no multiplications when done in a recursive fashion at equispaced arguments the evaluation of an exponential of a kth order polynomial can be accomplished by k multiplications and no additions or exponentiations combinations of rational functions and exponentials can therefore be realized very efficiently by combining these properties

stabilisation of hybrid stochastic systems with levy noise by discrete time feedback control this paper is devoted to deal with the stabilisation problems of continuous time hybrid stochastic systems often described by stochastic differential equations with markovian switching with levy

pth moment asymptotic stability for neutral stochastic functional differential equations with levy processes in this paper we will consider a class of neutral stochastic functional differential equations with levy processes levy processes contain a number of very important processes as special cases such as brownian motion the poisson process stable and self decomposable processes and subordinators and so on but its sample paths are discontinuity which makes the analysis more difficult in this paper we try to get over this difficulty the contributions of this paper are as follows a we will use lyapunov functional method to study the pth moment asymptotic stability and almost sure asymptotic stability of neutral stochastic functional differential equations with levy processes b under the result of a we will investigate two types of continuity of the solution continuous in the pth moment and continuous in probability finally we provide an example to illustrate the usefulness of the obtained results

efficient evaluation of multivariate polynomials over multidimensional grids let p x 1 x 2 x n be a multivariate polynomial in n variables x 1 x 2 x n and suppose that p x 1 x 2 x n is of degree m i in x i i 1 2 n it is shown how p x 1 x 2 x n may be evaluated at x i x 0i n i i for n i 0 1 2 and i 1 2 n using not more than m 1 m 2 m n additions per point feasibility of reduction from this upper bound is demonstrated in the n 2 case

an introduction to the regular theory of fairness abstract we present an approach to fairness in the style of the theory of regularity several concepts of fairness are researched and compared within the classical language theory of words of infinite length

infinite trees markings and well foundedness abstract a necessary and sufficient condition for a given marked tree to have no infinite paths satisfying a given formula is presented the formulas are taken from a language introduced by harel covering a wide scale of properties of infinite paths including most of the known notions of fairness this condition underlies a proof rule for proving that a nondeterministic program has no infinite computations satisfying a given formula interpreted over state sequences we also show two different forms of seemingly more natural necessary and sufficient conditions to be inadequate

stability analysis of neutral stochastic differential delay equations driven by levy noises abstract this paper mainly analyzes the well posedness and the stability analysis for the global solution of neutral stochastic differential delay equations nsddes driven by levy noises by using an integral lemma and a lyapunov function approach the existence and uniqueness theorem is proved then by using the inequality technique and the stochastic analysis theory the exponential stability in pth p 2 moment of such equations is discussed by using another integral lemma and using the baralat lemma as well as the stochastic analysis the almost surely asymptotic stability is also studied finally one example is given to check the effectiveness of the findings derived

a storage efficient method for solving banded toeplitz systems a method is presented for solving the banded toeplitz system tx y by decomposing t into its asymptotic upper and lower triangular factors which are banded and toeplitz and a rank p correction matrix where p is the bandwidth of t this way of representing t requires only o p sup 2 words of storage and allows computation of x in o 2np operations a similar method is presented for the case in which t is bi infinite and y is zero outside a finite region

polynomial phase signal analysis based on the polynomial derivatives decompositions an exact decomposition of the derivatives of any order of a polynomial spl phi t is proposed in terms of spl phi t t sub 0 spl phi t t sub n this result allows us to introduce generalized time frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase the relationships between these distributions and the already known polynomial distributions i e the polynomial phase transform and the polynomial wigner ville distribution are discussed illustrations by example are proposed

a multiparameter analysis of domino tiling with an application to concurrent systems abstract the complexities of two domino problems namely the n k domain problem and the n k 2 person domino game problem will be investigated with respect to parameters n and k simultaneously the former concerns itself with tiling a rectangle of width k in the cartesian plane using a given set of n domino types the latter involves two players taking turns to tile a rectangle of width k using a given set of n domino types in an antagonistic fashion we are interested in determining whether there is a winning strategy for the first player it turns out that the n k domino problem has upper and lower bounds of o k log n and k 6 2 logn nondeterministic space respectively for the n k 2 person domino game problem we are able to show upper and lower bounds of o n c k and n k 5 16 e deterministic time respectively for some constant c any e 0 and k 17 using the result concerning the 2 person domino game problem we then establish a lower bound of n k 7 16 e deterministic time any e 0 and k 21 for the lockout problem for systems of k communicating processes in which the size of each process is bounded by n this together with an o n d k deterministic time upper bound which will also be shown in this paper fully explains the role played by each of the two parameters n and k in the overall complexity of the problem it indicates that the upper bound is optimal with respect to parameters n and k

s plane to z plane mapping using a simultaneous equation algorithm based on the bilinear transformation this note presents an algorithm for transforming a continuous transfer function to an approximate discrete equivalent by means of the bilinear transformation

probabilistic termination versus fair termination note abstract in this note we show that probabilistic termination of concurrent programs is in many cases much simpler than the fair one for a wide class of definitions of probabilistic termination we may express termination by 0 2 arithmetic formula whereas the fair termination can be expressed only by second order arithmetic formula proof of fair termination usually needs induction on recursive ordinals but proof of probabilistic termination has the complexity equivalent to that of deterministic program termination

a note on almost sure asymptotic stability of neutral stochastic delay differential equations with markovian switching in this paper we consider neutral stochastic delay differential equations with markovian switching our key aim is to establish lasalle type stability theorems for the underlying equations the key techniques used in this paper are the method of lyapunov functions and the convergence theorem of nonnegative semi martingales the key advantage of our new results lies in the fact that our results can be applied to more general non autonomous equations

a note on efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments by a h nuttall a h nuttall s see ibid vol assp 35 no 10 p 1486 7 1987 algorithm for the evaluation of a polynomial at a large number of arguments is addressed the authors supplement nuttall s treatment of the problem by 1 giving a relationship between the coefficients of the original polynomial and those of the equivalent one in terms of the integer variable n and 2 by deriving a formula for the computation of the initial values required for nuttall s recursive procedure to commence as a result of these supplements the recursive algorithm is completely programmable and can be efficiently implemented for any order n of the polynomial some general observations are made on the computational complexity in recursive evaluation in contrast to direct evaluation of a polynomial

a note on exponential stability for impulsive neutral stochastic partial functional differential equations in this note the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique some sufficient conditions are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained result

on computing equally spaced samples of a complex gaussian function this correspondence extends the simple nonlinear recursion presented by kaiser in 3 to the fast generation of equally spaced samples of a complex gaussian chirp function exp c 0 c 1 t c 2 t 2 using only two complex multiplications per point

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

on the fast generation of equally spaced values of the gaussian function a exp at t this correspondence describes a very simple two term nonlinear recursion due to teager that can be used to efficiently generate a sequence of equally spaced values of the gaussian function a exp at t an extension of the method reduces the computation required to only two multiplications per point

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

on the statistics of fixed point roundoff error roundoff error after fixed point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal this paper presents a statistical analysis of fixed point roundoff error that identifies the conditions under which this model is valid and examines the statistical behavior of roundoff error when these conditions are not satisfied the results show that if the multiplier coefficient is expressed as a n m where m is a positive integral power of two and n is an odd integer then the errors generated by roundoff after multiplication can generally be modeled as uniformly distributed white and uncorrelated with the signal if the signal has sufficiently wide bandwidth and has a dynamic range that extends over approximately m quantum steps for narrow band low level signals the roundoff error statistics can differ significantly from the uniform white uncorrelated model in addition these results show that statistical behavior of roundoff error can differ significantly from that of the quantization error that is generated when a continuous random variable is quantized

a proof rule for fair termination of guarded commands we present a proof rule for fairly terminating guarded commands based on a well foundedness argument the rule is applied to several examples and proved to be sound and semantically complete w r t an operational semantics of computation trees the rule is related to another rule suggested by lehmann pnueli and stavi in proc internat colloq automata lang and programming 81 acre july 1981 by showing that the semantic completeness of the lps rule follows from the completeness or ours

existence and stability of solutions to non lipschitz stochastic differential equations driven by levy noise in this paper successive approximation method is applied to investigate the existence and uniqueness of solutions to stochastic differential equations sdes driven by levy noise under non lipschitz condition which is a much weaker condition than lipschitz one the stability of solutions to non lipschitz sdes driven by levy noise is also considered and the stochastic stability is obtained in the sense of mean square

a relationship between the z transform and the fourier transform a relationship between the one sided z transform and the one sided discrete time fourier transform is discussed every discrete time function that can result from the sampling of a periodic continuous time function is considered to be periodic a simple general equation is presented and discussed

a simple algorithm for arbitrary polynomial transformation a very simple algorithm is developed for the arbitrary rational transformation of a polynomial the fact that many of the multiplications performed involve one zero factor is not explicitly taken into account if desired this could be done with some increase in the complexity of the algorithm itself finally if roundoff error is expected to be a problem double precision arithmetic could be used

estimating the doa and the polarization of a polynomial phase signal using a single polarized vector sensor this paper introduces a novel algorithm to estimate the direction of arrival doa and the polarization of a completely polarized polynomial phase signal of an arbitrary degree the algorithm utilizes a polarized vector sensor comprising a spatially collocated six component electromagnetic vector sensor a dipole triad or a loop triad this esprit based algorithm is based on a time invariant matrix pencil pair derived from the time delayed data sets collected by a single polarized vector sensor the high order difference function of the signal s phase constructs the invariant factor used in the esprit algorithm the steering vector is estimated from the signal subspace eigenvector of the data correlation matrix following which the closed form doa and polarization can be obtained given the degree of the polynomial phase signal this approach resolves the two dimensional azimuth elevation angle and the polarization of the source and requires neither a priori knowledge of the polynomial phase signal s coefficients nor a priori knowledge of the polynomial phase signal s frequency spectrum the efficacy of the proposed algorithm is verified by monte carlo simulations estimation accuracies of the doa and the polarization parameters are evaluated by the closed form cramer rao bounds which are independent of the polynomial coefficients the degree of the polynomial phase signal and the azimuth angle of the source

hoare s logic for nondeterministic regular programs a nonstandard approach abstract this paper studies hoare s logic for nondeterministic regular programs with unbounded nondeterminism from the point of view of nonstandard dynamic logic we define a so called continuous semantics which allows certain infinitely long computations and compare it with usual semantics proving among other things the equivalence of both over reasonable data types we also establish a completeness theorem for hoare s calculus relative to continuous semantics thereby generalizing a previous result of csirmaz the proof makes use of a normal form for regular programs which is perhaps interesting in its own right

complexity of tile rotation problems in this paper we introduce tile rotation problems the instances or initial configurations are tile assignments on a n x n lattice board and the question to be answered is the following does there exist any configuration obtained horn the initial one by tile rotations only whose cost is less than a given bound notice that a zero cost configuration corresponds to a perfect tiling we prove here the np completeness for both the zero cost problem for a particular set of 5 tiles and the minimization problem for a particular set of 2 tiles finally by showing the polynomiality of some subproblems we establish complexity border results

on fixed point roundoff error analysis the author points out the existence of work published by the author us dept of commerce tech rep ad a086826 57 pp apr 1980 prior to the appearance of the paper by barnes et al ibid vol assp 33 p 595 606 june 1985 covering the same subject

defining fairness in reactive and concurrent systems we define when a linear time temporal property is a fairness property with respect to a given system this captures the essence shared by most fairness assumptions that are used in the specification and verification of reactive and concurrent systems such as weak fairness strong fairness k fairness and many others we provide three characterizations of fairness a language theoretic a game theoretic and a topological characterization it turns out that the fairness properties are the sets that are large from a topological point of view that is they are the co meager sets in the natural topology of runs of a given system this insight provides a link to probability theory where a set is large when it has measure 1 while these two notions of largeness are similar they do not coincide in general however we show that they coincide for regular properties and bounded borel measures that is an regular temporal property of a finite state system has measure 1 under a bounded borel measure if and only if it is a fairness property with respect to that system the definition of fairness leads to a generic relaxation of correctness of a system in linear time semantics we define a system to be fairly correct if there exists a fairness assumption under which it satisfies its specification equivalently a system is fairly correct if the set of runs satisfying the specification is topologically large we motivate this notion of correctness and show how it can be verified in a system

existence uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps in this paper we are concerned with neutral stochastic functional differential equations driven by pure jumps nsfdewpjs we prove the existence and uniqueness of the solution to nsfdewpjs whose coefficients satisfying the local lipschitz condition in addition we establish the p th exponential estimations and almost surely asymptotic estimations of the solution for nsfdewjs

edge preserving filtering by combining nonlinear mean and median filters a very general class of nonlinear filters called mapping order statistics filters mosfs is introduced a subclass of the mosfs called l sub p mean median filters l sub p mmfs is discussed the l sub p mmf shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters in the analysis of the deterministic properties of the l sub p mmf the concept of a monotonic trend region is introduced a necessary condition for a signal to be a root signal is given this necessary condition is also valid for the known finite impulse response median hybrid filter

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

fairness distances and degrees abstract we show the identity between sets of fair computations in recursive transition graphs sets of cluster points of finite computations for 01 ultra metrics refining the baire metrics and 03 subsets of the results are applied to recursive marked trees fairness definitions regular languages and 03 sets

a taxonomy of fairness and temporal logic problems for petri nets in this paper we define a temporal logic for reasoning about petri nets we show the model checking problem for this logic to be ptime equivalent to the petri net reachability problem using this logic and two refinements we show the fair nontermination problem to be ptime equivalent to reachability for several definitions of fairness for other versions of fairness this problem is shown to be either ptime equivalent to the boundedness problem or highly undecidable in all 24 versions of fairness are examined

the power of temporal proofs abstract some methods for reasoning about concurrent programs and hardware devices have been based on proof systems for temporal logic unfortunately all effective proof systems for temporal logic are incomplete for the standard semantics in the sense that some formulas hold in every intended model but cannot be proved we evaluate and compare the power of several proof systems for temporal logic specifically we relate temporal systems to classical systems with explicit time parameters a typical temporal system turns out to be incomplete in a strong sense we exhibit a short valid formula it fails to prove we suggest the addition of new rules to define auxiliary predicates with these rules we obtain nonstandard soundness and completeness results in particular one of the simple temporal systems we describe is as powerful as peano arithmetic

new efficient ls and svd based techniques for high resolution frequency estimation new least squares and singular value decomposition based methods for the estimation of the frequencies of complex sinusoids in white noise are presented the methods are based on a new symmetric prediction problem that has some very useful properties leading to algorithms that have considerably reduced complexity the new symmetric predictor is superior in performance as compared to the well known symmetric smoother and has a performance comparable to other well known methods finally a new ls based method which combines the new prediction technique with the fblp method is proposed this method performs slightly better than the fblp offering at the same time a significant computational saving as a by product in the derivation of the new methods is the establishment of some useful properties concerning the eigenstructure of hermitian and persymmetric matrices

new result on exponential stability for neutral stochastic linear system with time varying delay abstract this paper mainly considers the problem for the exponential stability of neutral stochastic linear system with time varying delay in the light of a coupled delay integral inequality and using the stochastic analytic technique the exponential stability criteria for such systems are given in term of the algebraic inequalities regardless of whether the time varying delay is differentiable or not an illustrative numerical example is given to show the effectiveness of the obtained result

undecidability of bisimilarity by defender s forcing stirling l1996 1998r proved the decidability of bisimilarity on so called normed pushdown processes this result was substantially extended by senizergues l1998 2005r who showed the decidability of bisimilarity for regular or equational graphs of finite out degree this essentially coincides with weak bisimilarity of processes generated by unnormed pushdown automata where the e transitions can only deterministically pop the stack the question of decidability of bisimilarity for the more general class of so called type 1 systems which is equivalent to weak bisimilarity on unrestricted e popping pushdown processes was left open this was repeatedly indicated by both stirling and senizergues here we answer the question negatively that is we show the undecidability of bisimilarity on type 1 systems even in the normed case we achieve the result by applying a technique we call defender s forcing referring to the bisimulation games the idea is simple yet powerful we demonstrate its versatility by deriving further results in a uniform way first we classify several versions of the undecidable problems for prefix rewrite systems or pushdown automata as 01 complete or 11 complete second we solve the decidability question for weak bisimilarity on pa process algebra processes showing that the problem is undecidable and even 11 complete third we show 11 completeness of weak bisimilarity for so called parallel pushdown or multiset automata a subclass of labeled place transition petri nets