Do we really need common variable orders for synthesizing OBDDs?

OBDDs have already proved useful in the verification of combinatorial and sequential circuits. But for the..

One Step Further: Extending Electronic Submission Into the Reviewing Process

Modern information technologies have vastly improved the efficiency of document handling, and provide additional features and functionalities. In most cases, this improvement was realized by simply replacing traditional tools by their electronic counterparts, and finding good uses for the added possibilities. However, there are cases where adherence to the established structures, most notably the actual document workflow, does not allow optimal use of the potential; adapting and redesigning workflows so as to better fit the capabilities of the new tools allows to further augment performance. In the academic environment, two prime examples of the use of information technology for document processing are scientific journals and conference proceedings. In addition to being genuinely multi-authored documents, the authors contributing to these collections are usually distributed across a significant part of the globe. As a result, academia has eagerly adopted, over the last years, the devel..

On Boolean vs. Modular Arithmetic for Circuits and Communication Protocols

We compare two computational models that appeared in the literature in a Boolean setting and in an analog setting based on modular arithmetic. We prove that in both cases the arithmetic version can to some extend simulate the Boolean version. Although the models are very different, the proofs rely on the same idea based on the Schwartz-Zippel-Theorem. In the first part we give a new simulation of semi-unbounded Boolean circuits by semiunbounded circuits with unbounded parity gates. Our simulation is simpler and more efficient with respect to depth than the original simulation of G'al and Wigderson [4]. In the second part we prove, that two-party parity communication protocols can approximate nondeterministic communication protocols. A strict simulation of one by the other is impossible as was shown in [3]. 1 Introduction We present two randomized simulations of Boolean computational models by their corresponding "parity" models. The first results of this kind are due to [5, 4], who pr..

OBDD-based Verification of Communication Protocols - Methods for the Verification of Data Link Protocols

The demand for formal verification of communication protocols is increasing since the use of distributed systems is still rapidly growing. Ordered binary decision diagrams (OBDDs) are widely and successfully used in the area of digital circuit verification. This suggests an application of OBDD techniques to the verification of protocols, but the formal modelling of a complete protocol is too complex for a verification with OBDDs using current techniques. Therefore, the model has to be restricted. The model we are using is as least restricted as needed and preserves as much of the protocol's properties as possible. Since there is no further knowledge about protocol verification using OBDD techniques, we decided to use two common data link protocols to gain experience. The experimental results are leading to an approach to the problem of finding well suited orders of input variables needed for an efficient OBDD representation. Furthermore, we introduce a technique for avoiding time consu..

Parallel versus Sequential Task-Processing: A New Performance Model in Discrete Time

A main question in parallel computing is the following: Under which conditions should parallel task-processing be preferred to sequential task-processing. In this paper we present stochastic models for the evaluation of the mean time between the creation of a task and the end of its processing. The models are based on the theory of queueing systems in discrete time. We consider closed tandem networks with state-dependent task creation probabilities and bulk arrivals. One of these networks includes a bulk server, another one has state-dependent service completion probabilities approximating the concatenation of a single server station and an inønite server, both with deterministic service times. Analytical and numerical results, which give an answer to the question above, are presented. Keywords: Parallel computing, performance evaluation, queueing networks in discrete time. 1 Introduction Recent research in parallel computing deals with the implementation of algorithms for handling se..

Binary Decision Diagrams and the Multiple Variable Order Problem

Ordered Binary Decision Diagrams (OBDDs) are the first choice for representation and manipulation of Boolean functions in CAD. Since the size of an OBDD heavily depends on its variable order, much effort is spent on the computation of good variable orders and their improvement. When applying common optimization techniques one often has to cope with different variable orderings, e.g., in sequential analysis for representing transition relation and reachable state set, where further efficient manipulation requires a common variable order. In this paper we propose some solutions of the multiple variable order problem that are based on heuristics for the computation of a well suited intermediate variable ordering

Circuit and Decision Tree Complexity of Some Number Theoretic Problems

We extend the area of applications of the Abstract Harmonic Analysis to lower bounds on the circuit and decision tree complexity of Boolean functions related to some number theoretic problems. In particular, we prove that deciding if a given integer is square-free and testing co-primality of two integers by unbounded fan-in circuits of bounded depth requires superpolynomial size. 1 Introduction In recent years spectral techniques based on the Abstract Harmonic Analysis on the hypercube have been shown to represent a very useful tool for obtaining lower complexity bounds. Various links between Fourier coefficients of Boolean functions and their complexity characteristics have been studied in a number of works, see [1, 2, 3, 4, 6, 8, 13, 19, 20, 22, 23]. In particular, these spectral techniques have been successfully applied to the parity function and to threshold functions. Institut fur Informatik, Technische Universitat Munchen, D-80290 Munchen, Germany. [email protected]..

On Alternating vs. Parity Communication Complexity

We prove that for any O(1)-alternating communication protocol of length L computing a function f and for 0 ! ffi there is a parity communication protocol of length O((L \Gamma log ffi ) O(1) ) computing a function differing from f in at most a ffi -fraction of the inputs. This can be generalized to computations based on arithmetic over any finite field. A consequence is a new proof and improvement of a connection between matrix rigidity over finite fields and alternating communication complexity that was first observed by Razborov [Raz89]. As a side result we prove upper bounds on the rigidity over any field of a 0-1-matrix A in terms of the numbers of constant submatrices required to cover A. Keywords: Communication complexity, Approximation method, Randomized proof of existence, Matrix rigidity 1 Introduction Alternating communication protocols where introduced by Babai et al. [BFS86] and generalize the following base model: Two players share an input (x; y) (where access is res..

Symmetric Functions in AC 0 [2]

We consider symmetric Boolean functions computable by polynomial size constant depth circuits with AND-, OR-, and PARITY-gates. If the depth is restricted to 2 or if PARITY-gates are disallowed characterizations of these functions are already known. Under the assumption that a certain transformation on the set of Boolean functions is complexity-preserving we can give a complete characterization: any symmetric Boolean function in AC 0 [2] is "in essential" 2 t -periodic with 2 t = log O(1) n. 1 Introduction One of the main challenges of complexity theory is the derivation of strong lower bounds to the circuit complexity of concrete computational problems. Although many research work is done in this field, progress is very slow. Currently attacks concentrate on complexity classes between AC 0 and TC 0 . Of special interest are classes like AC 0 [m] corresponding to polynomial size constant depth circuits with AND-, OR-, and MODm -gates (the latter ones computing 1 iff the ..