159 research outputs found
10271 Abstracts Collection -- Verification over discrete-continuous boundaries
From 4 July 2010 to 9 July 2010, the Dagstuhl Seminar 10271
``Verification over discrete-continuous boundaries\u27\u27
was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Recommended from our members
Function Verification of Combinational Arithmetic Circuits
Hardware design verification is the most challenging part in overall hardware design process. It is because design size and complexity are growing very fast while the requirement for performance is ever higher. Conventional simulation-based verification method cannot keep up with the rapid increase in the design size, since it is impossible to exhaustively test all input vectors of a complex design. An important part of hardware verification is combinational arithmetic circuit verification. It draws a lot of attention because flattening the design into bit-level, known as the bit-blasting problem, hinders the efficiency of many current formal techniques. The goal of this thesis is to introduce a robust and efficient formal verification method for combinational integer arithmetic circuit based on an in-depth analysis of recent advances in computer algebra. The method proposed here solves the verification problem at bit level, while avoiding bit-blasting problem. It also avoids the expensive Groebner basis computation, typically employed by symbolic computer algebra methods. The proposed method verifies the gate-level implementation of the design by representing the design components (logic gates and arithmetic modules) by polynomials in Z2n . It then transforms the polynomial representing the output bits (called “output signature”) into a unique polynomial in input signals (called “input signature”) using gate-level information of the design. The computed input signature is then compared with the reference input signature (golden model) to determine whether the circuit behaves as anticipated. If the reference input signature is not given, our method can be used to compute (or extract) the arithmetic function of the design by computing its input signature. Additional tools, based on canonical word-level design representations (such as TED or BMD) can be used to determine the function of the computed input signature represents. We demonstrate the applicability of the proposed method to arithmetic circuit verification on a large number of designs
Algorithmically generating new algebraic features of polynomial systems for machine learning
There are a variety of choices to be made in both computer algebra systems
(CASs) and satisfiability modulo theory (SMT) solvers which can impact
performance without affecting mathematical correctness. Such choices are
candidates for machine learning (ML) approaches, however, there are
difficulties in applying standard ML techniques, such as the efficient
identification of ML features from input data which is typically a polynomial
system. Our focus is selecting the variable ordering for cylindrical algebraic
decomposition (CAD), an important algorithm implemented in several CASs, and
now also SMT-solvers. We created a framework to describe all the previously
identified ML features for the problem and then enumerated all options in this
framework to automatically generation many more features. We validate the
usefulness of these with an experiment which shows that an ML choice for CAD
variable ordering is superior to those made by human created heuristics, and
further improved with these additional features. We expect that this technique
of feature generation could be useful for other choices related to CAD, or even
choices for other algorithms with polynomial systems for input.Comment: To appear in Proc SC-Square Workshop 2019. arXiv admin note:
substantial text overlap with arXiv:1904.1106
3-torsion and conductor of genus 2 curves
We give an algorithm to compute the conductor for curves of genus 2. It is
based on the analysis of 3-torsion of the Jacobian for genus 2 curves over
2-adic fields.Comment: 16 page
New Baselines for Local Pseudorandom Number Generators by Field Extensions
We will revisit recent techniques and results on the cryptoanalysis of local pseudorandom number generators (PRGs). By doing so, we will achieve a new attack on PRGs whose time complexity only depends on the algebraic degree of the PRG. Concretely, for PRGs , we will give an algebraic algorithm that distinguishes between random points and image points of , whose time complexity is bounded by
and whose advantage is at least in the worst case.
To the best of the author\u27s knowledge, this attack outperforms current attacks on the pseudorandomness of local random functions with guaranteed noticeable advantage and gives a new baseline algorithm for local PRGs. Furthermore, this is the first subexponential attack that is applicable to polynomial PRGs of constant degree over fields of any size with a guaranteed noticeable advantage.
We will extend this distinguishing attack further to achieve a search algorithm that can invert a uniformly random constant-degree map with high advantage in the average case. This algorithm has the same runtime complexity as the distinguishing algorithm
A Mathematical Framework for Agent Based Models of Complex Biological Networks
Agent-based modeling and simulation is a useful method to study biological
phenomena in a wide range of fields, from molecular biology to ecology. Since
there is currently no agreed-upon standard way to specify such models it is not
always easy to use published models. Also, since model descriptions are not
usually given in mathematical terms, it is difficult to bring mathematical
analysis tools to bear, so that models are typically studied through
simulation. In order to address this issue, Grimm et al. proposed a protocol
for model specification, the so-called ODD protocol, which provides a standard
way to describe models. This paper proposes an addition to the ODD protocol
which allows the description of an agent-based model as a dynamical system,
which provides access to computational and theoretical tools for its analysis.
The mathematical framework is that of algebraic models, that is, time-discrete
dynamical systems with algebraic structure. It is shown by way of several
examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog
Algorithmic boundedness-from-below conditions for generic scalar potentials
Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results
- …