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Yu-Wei Fan

Publications and source records attributed to Yu-Wei Fan.

At least 19 recordsLinked to original sources

Efficient Hardware Information-Flow Tracking for Pre-Silicon Security Testing

Register-Transfer Level (RTL) simulation is widely used to test hardware before it is fabricated. To allow testing for security related information flow properties, such as confidentiality and integrity, taint logic can be automatically added to the design to track how information flows through it. However, taint logic instrumented by the state-of-the-art, such as CellIFT, makes simulation-based testing prohibitively expensive: On our evaluation of Mega-BOOM (136K cells), it increases the instrumented design to 5.81x the original cell count and causes a 143.72x simulation slowdown. The taint logic could be simplified to improve simulation speed, but it will inevitably trade off its precision. This lightweight, imprecise taint logic will introduce false positives and may eventually result in even more overhead to check these false positives. This paper explores the research question of where precision is actually needed in the design to overcome the overhead of false positives. It presents CEGAR-T, a framework that automatically synthesizes taint logic that minimizes the taint-logic instrumentation overhead while guaranteeing no false positives (relative to the precise CellIFT baseline). We have implemented CEGAR-T and evaluated it on the safe instruction set problem for timing side-channel security across open-source RISC-V cores. Over all evaluated cores, CEGAR-T reduces both instrumentation and simulation overhead, in geometric-mean, from 5.64x to 1.42x and from 34.65x to 1.79x, respectively, without compromising the precision benefit of the CellIFT baseline.

cs.CR

Notes on the deformed Hermitian-Yang-Mills equations and the large scaling limits of stability conditions

In this short note, we show that, assuming a conjecture of Arcara and Miles, a line bundle on a smooth complex projective surface admits a deformed Hermitian-Yang-Mills metric if and only if it is stable in the ``large scaling limit" with respect to a generic K\"ahler form. The same statement for toric surfaces was recently proved by Stoppa. The purpose of this note is to remark that this equivalence holds for arbitrary smooth projective surfaces.

math.AG

Mirror symmetry for lattice-polarized abelian surfaces

Inspired by the Dolgachev-Nikulin-Pinkham mirror symmetry for lattice-polarized K3 surfaces, we study its analogue for abelian surfaces. In this paper, we introduce lattice-polarized abelian surfaces and construct their coarse moduli spaces. We then construct stringy K\"ahler moduli spaces for abelian surfaces and show that these two spaces are naturally identified for mirror pairs. We also introduce a natural involution on stringy K\"ahler moduli spaces which, under mirror symmetry, pairs abelian surfaces and their duals. Finally, we determine conditions for the existence of mirror partners and classify self-mirror abelian surfaces via their N\'eron-Severi lattices.

math.AG

Special Lagrangians and Bridgeland stable objects beyond geometric stability conditions: the product case

We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical K\"unneth formulae. These stability conditions correspond to certain holomorphic volume forms, under which we prove that every stable object admits a special Lagrangian representative. This provides the first higher-dimensional examples of stability conditions away from the large complex structure limit for which ``stable implies special Lagrangian" is proved.

math.SG

SecIC3: Customizing IC3 for Hardware Security Verification

Recent years have seen significant advances in using formal verification to check hardware security properties. Of particular practical interest are checking confidentiality and integrity of secrets, by checking that there is no information flow between the secrets and observable outputs. A standard method for checking information flow is to translate the corresponding non-interference hyperproperty into a safety property on a self-composition of the design, which has two copies of the design composed together. Although prior efforts have aimed to reduce the size of the self-composed design, there are no state-of-the-art model checkers that exploit their special structure for hardware security verification. In this paper, we propose SecIC3, a hardware model checking algorithm based on IC3 that is customized to exploit this self-composition structure. SecIC3 utilizes this structure in two complementary techniques: symmetric state exploration and adding equivalence predicates. We implement SecIC3 on top of two open-source IC3 implementations and evaluate it on a non-interference checking benchmark consisting of 10 designs. The experiment results show that SecIC3 significantly reduces the time for finding security proofs, with up to 49.3x proof speedup compared to baseline implementations.

cs.CR

A space of stability conditions that is not a length space

We prove that the space of Bridgeland stability conditions, when equipped with the canonical metric, is not a length space in general. This resolves a question posed by Kikuta in the negative. Furthermore, we introduce two modified metrics on the stability spaces, which may exhibit better metric properties.

math.AG

Shifting numbers of abelian varieties via bounded t-structures

The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincare translation numbers that are widely used in dynamical systems. Motivated by this analogy, Fan-Filip raised the following question: ``Do the shifting numbers define a quasimorphism on the group of autoequivalences of a triangulated category?" An affirmative answer was given by Fan-Filip for the bounded derived category of coherent sheaves on an elliptic curve or an abelian surface, via properties of the spaces of Bridgeland stability conditions on these categories. We prove in this article that the question has an affirmative answer for abelian varieties of arbitrary dimensions, generalizing the result of Fan-Filip. One of the key steps is to establish an alternative definition of the shifting numbers via bounded t-structures on triangulated categories. In particular, the full package of a Bridgeland stability condition (a bounded t-structure, and a central charge on a charge lattice) is not necessary for the purpose of computing the shifting numbers.

math.DS

Nielsen realization problem for derived automorphisms of generic K3 surfaces

We prove that all nontrivial finite subgroups of derived automorphisms of K3 surfaces of Picard number one have order two and give formulas for the numbers of their conjugacy classes. We also obtain a similar result for the subgroups which are finite up to shifts. This in turn shows that such a K3 surface admits an associated cubic fourfold if and only if it has a derived automorphism of order three up to shifts. These results are achieved by proving that such a subgroup fixes a Bridgeland stability condition up to $\mathbb{C}$-actions. We also establish similar existence results for curves, twisted abelian surfaces, generic twisted K3 surfaces, and standard autoequivalences on surfaces.

math.AG

Counting special Lagrangian classes and semistable Mukai vectors for K3 surfaces

Motivated by the study of the growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one generalization, we give a result regarding the upper bound on the asymptotics of the number of classes of irreducible special Lagrangians in K3 surfaces with bounded period integrals. In another generalization, we give the exact leading term in the asymptotics of the number of Mukai vectors of semistable coherent sheaves on algebraic K3 surfaces with bounded central charges, with respect to generic Bridgeland stability conditions.

math.AG

Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds

We investigate the complex and Kähler attractor mechanisms of moduli spaces of Calabi-Yau 3-folds. The complex attractor mechanism was previously studied by Ferrara-Kallosh-Strominger, Moore and others in string theory. It is concerned with the minimizing problems of the normalized central charges of 3-cycles and defines a new interesting class of Calabi-Yau 3-folds called, the complex attractor varieties. In light of mirror symmetry, we introduce the Kähler attractor mechanism and define the Kähler attractor varieties. The complex and Kähler attractor varieties are expected to possess very rich structures, in particular certain complex and Kähler rigidities.

math.AG

Categorical polynomial entropy

For classical dynamical systems, the polynomial entropy serves as a refined invariant of the topological entropy. In the setting of categorical dynamical systems, that is, triangulated categories endowed with an endofunctor, we develop the theory of categorical polynomial entropy, refining the categorical entropy defined by Dimitrov-Haiden-Katzarkov-Kontsevich. We justify this notion by showing that for an automorphism of a smooth projective variety, the categorical polynomial entropy of the pullback functor on the derived category coincides with the polynomial growth rate of the induced action on cohomology. We also establish in general a Yomdin-type lower bound for the categorical polynomial entropy of an endofunctor in terms of the induced endomorphism on the numerical Grothendieck group of the category. As examples, we compute the categorical polynomial entropy for some standard functors like shifts, Serre functors, tensoring line bundles, automorphisms, spherical twists, P-twists, and so on, illustrating clearly how categorical polynomial entropy refines the study of categorical entropy and enables us to study the phenomenon of categorical trichotomy. A parallel theory of polynomial mass growth rate is developed in the presence of Bridgeland stability conditions.

math.AG

Surfaces, braids, Stokes matrices, and points on spheres

Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus surfaces, by establishing exceptional isomorphisms with certain moduli of local systems. This relies on the existence of group structure for spheres in these dimensions. We also use the connection to demonstrate that the space of rank 4 Stokes matrices with fixed Coxeter invariant of nonzero discriminant contains only finitely many integral braid group orbits.

math.AG

Asymptotic shifting numbers in triangulated categories

We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that are widely used in dynamical systems. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Additionally, we relate our shifting numbers to the entropy function introduced by Dimitrov, Haiden, Katzarkov, and Kontsevich.

math.AG

New rational cubic fourfolds arising from Cremona transformations

Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation defined by the Veronese surface. By studying how these maps act on the cubics known to be rational, we surprisingly found new rational examples.

math.AG

Contractibility of space of stability conditions on the projective plane via global dimension function

We compute the global dimension function $\mathrm{gldim}$ on the principal component $\mathrm{Stab}^{\dag}(\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\mathrm{gldim}^{-1}(2)$ is contained in the closure $\bar{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions. We show that $\mathrm{gldim}^{-1}[2,x)$ contracts to $\mathrm{gldim}^{-1}(2)$ for any real number $x\geq 2$ and that $\mathrm{gldim}^{-1}(2)$ is contractible.

math.AG

On pseudo-Anosov autoequivalences

Motivated by results of Thurston, we prove that any autoequivalence of a triangulated category induces a filtration by triangulated subcategories, provided the existence of Bridgeland stability conditions. The filtration is given by the exponential growth rate of masses under iterates of the autoequivalence, and only depends on the choice of a connected component of the stability manifold. We then propose a new definition of pseudo-Anosov autoequivalences, and prove that our definition is more general than the one previously proposed by Dimitrov, Haiden, Katzarkov, and Kontsevich. We construct new examples of pseudo-Anosov autoequivalences on the derived categories of quintic Calabi-Yau threefolds and quiver Calabi-Yau categories. Finally, we prove that certain pseudo-Anosov autoequivalences on quiver 3-Calabi-Yau categories act hyperbolically on the space of Bridgeland stability conditions.

math.AG

Entropy of an autoequivalence on Calabi-Yau manifolds

We prove that the categorical entropy of the autoequivalence $T_{\mathcal{O}}\circ(-\otimes\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $λ$ satisfying $$ \sum_{k\geq 1}\frac{χ(\mathcal{O}(k))}{e^{kλ}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.

math.AG