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Compositional Invariant Generation via Linear Recurrence Analysis
[article]
2015
arXiv
pre-print
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This paper presents a new method for automatically generating numerical invariants for imperative programs. ...
Our experiments demonstrate that on verification tasks, our method is competitive with leading invariant generation and verification tools. ...
Non-linear invariant generation is not the main focus of our work, but it is sometimes a necessary intermediate step for proving linear invariants in a compositional setting: since our analysis cannot ...
arXiv:1502.00138v1
fatcat:vlyjzek2pzflrhruwg6jytdr2q
Algebraic Program Analysis
[chapter]
2021
Lecture Notes in Computer Science
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It explains the foundations of algebraic program analysis, its strengths and limitations, and gives examples of algebraic program analyses for numerical invariant generation and termination analysis. ...
AbstractThis paper is a tutorial on algebraic program analysis. ...
The class of linear recurrence inequations considered in this example can be generalized in various ways to yield more powerful invariant generation procedures. ...
doi:10.1007/978-3-030-81685-8_3
fatcat:375brjonbbgfdfwpp72juwnljq
Templates and Recurrences: Better Together
[article]
2020
arXiv
pre-print
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This disadvantage is particularly prominent for non-linear invariant generation, because the user must supply maximum degrees on polynomials, bases for exponents, etc. ...
However, a disadvantage of past recurrence-based invariant-generation methods is that they are primarily loop-based analyses: they use recurrences to relate the pre-state and post-state of a loop, so it ...
This technique is used in the recurrence-based invariant generator ICRA to handle linear recursion [24] . ...
arXiv:2003.13515v1
fatcat:7nyzynmogzfyhdx32upifjlyy4
Non-linear reasoning for invariant synthesis
2017
Proceedings of the ACM on Programming Languages
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Automatic generation of non-linear loop invariants is a long-standing challenge in program analysis, with many applications. ...
Compositional recurrence analysis (CRA) [Farzan and Kincaid 2015] is another line of work, which focuses on over-approximate analysis of general loops rather than precise analysis of syntactically restricted ...
The following program illustrates the relevance of non-linear invariant generation to resource-bound analysis. ...
doi:10.1145/3158142
dblp:journals/pacmpl/KincaidCBR18
fatcat:rzj7q45oi5aihjxhduy7e6suqu
Page 392 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 63, Issue 6
[page]
1957
American Mathematical Society. Bulletin of the American Mathematical Society
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Results: solution of the long-standing problem of Hopf; connections between r.t. and electromagnetic theory via generalized harmonic analysis; connections be- tween r.t. and Mueller phenomenological optics ...
The principle of relativity has far reaching consequences in the form of invariance requirements for general con- stitutive equations, i.e. equations describing the mechanical properties of general classes ...
Index
2004
Journal of symbolic computation
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Sylvester sums for subresultants and multi-Schur functions, 689 LEMAIRE, F., An orderly linear PDE system with analytic initial conditions with a nonanalytic solution, 487 Linear recurrent sequences and ...
II, 153 MIGNOTTE, M. and Ş TEFȂNESCU, D., Linear recurrent sequences and polynomial roots, 637 Modular algorithms for computing Gröbner bases, 403 MORA, T. and SALA, M., On the Gröbner bases of some symmetric ...
doi:10.1016/s0747-7171(03)00152-4
fatcat:gnptdsf7grf75aoiujuxvve46a
Differential Invariants for Lie Pseudo-groups
[chapter]
2007
Gröbner Bases in Symbolic Analysis
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As a consequence, the recurrence formulas (5.11) for the non-phantom invariants do not in general directly yield the leading order normalized differential invariants in terms of lower order invariants ...
obtained via Lie's algorithm [51] . ...
The monomials in N |z (∞) index the complete system of functionally independent basic differential invariants, whereas the complementary monomials in K |z (∞) index the constant phantom differential invariants ...
doi:10.1515/9783110922752.217
fatcat:z2ui2d52zrg7ba56cczza2odjy
Koopman Operator Dynamical Models: Learning, Analysis and Control
[article]
2021
arXiv
pre-print
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2021 accepted arXiv:2102.02522v2 fatcat:sfcjxxky5vffbn2t7p3utsnpva
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. ...
In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework. ...
Representations via the Koopman paradigm generalize the notion of mode analysis from linear to nonlinear systems allowing for amendable relevance determination of the constituents of the full dynamics ...
arXiv:2102.02522v1
fatcat:wtjh3w6xmvbkvg4lz2cncmehyy
An Algebraic Framework for Compositional Program Analysis
[article]
2013
arXiv
pre-print
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This style of compositional loop analysis can yield interesting ways of computing loop invariants that cannot be defined iteratively. ...
A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program is computed by dividing it into sub-programs, computing their meaning, and then combining ...
Linear Recurrence Analysis Let us refer to our implementation of the linear recurrence analysis as LRA. ...
arXiv:1310.3481v1
fatcat:42sj26xl5jbe5iasdgczyi4vpe
Umbral Calculus and Cancellative Semigroup Algebras
[article]
2000
arXiv
pre-print
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We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures ...
Keywords: cancellative semigroups, umbral calculus, harmonic analysis, token, convolution algebra, integral transform ...
Let we have a shift invariant operator S. Clearly that its composition lf = ǫSf = [Sf ](e) with the augmentation is a linear functional. ...
arXiv:funct-an/9704001v2
fatcat:qq6fjy4f5vg3bjeejipfw3hwku
Kernel-Based Approaches for Sequence Modeling: Connections to Neural Methods
[article]
2019
arXiv
pre-print
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We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. ...
Our analysis provides a new perspective on the LSTM, while also extending it to n-gram convolutional filters. ...
However, the recurrent neural network (RNN) has also received renewed interest for analysis of sequential data. ...
arXiv:1910.04233v1
fatcat:2nk2lqjv5rgvtbpdq6lftbaq6u
Foreword to the Special Focus on Advances in Symbolic and Numeric Computation III
2020
Mathematics in Computer Science
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On a 2-Orthogonal Polynomial Sequence via Quadratic Decomposition
Teresa Augusta Mesquita In this work a symbolic approach of the general quadratic decomposition of polynomial sequences is applied to ...
To this purpose, this paper introduces a fractional order SIRS epidemic model with non-linear incidence rate. ...
doi:10.1007/s11786-020-00487-9
fatcat:e6zckweekncalpr6imbyfredjm
Umbral Calculus and Cancellative Semigroup Algebras
2000
Zeitschrift für Analysis und ihre Anwendungen
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We use them in Section 4 to describe principal combinatorial objects like delta families, generating functions, and recurrence operators. ...
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures ...
The essential part of the paper was written while author's stay at the Department of Mathematical Analysis, University of Ghent, as a Visiting Postdoctoral Fellow of the FWO-Vlaanderen (Fund of Scientific ...
doi:10.4171/zaa/953
fatcat:sd4ds5vohzbgbkwwrtx6u7475m
Linear Convergence of Comparison-based Step-size Adaptive Randomized Search via Stability of Markov Chains
[article]
2016
arXiv
pre-print
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Harrisrecurrence, geometric ergodicity) and thus define a general methodologyfor proving global linear convergence of CB-SARS algorithms onscaling-invariant functions. ...
On scaling-invariant functions, we show the existence of ahomogeneous Markov chain, as a consequence of natural invarianceproperties of CB-SARS (essentially scale-invariance and invariance tostrictly increasing ...
We believe that the author's analysis however is difficult to generalize to our context. ...
arXiv:1310.7697v6
fatcat:kokudy6yjjhqlfaadjs6vwzkwe
Moving Frames for Lie Pseudo--Groups
2008
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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The moving frame provides an effective means for determining complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, and solving ...
generators obtained via Lie's algorithm, [13, 14, 37, 38, 47] . ...
Infinitesimal Generators. Our subsequent analysis will rely heavily on the infinitesimal generators of the pseudogroup action. ...
doi:10.4153/cjm-2008-057-0
fatcat:rtyh47funrch3jwxzu73cfxqfq
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