@article{22648,
  abstract     = {Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems—a young but already well-established theory. We introduce the Conley–Morse persistence barcode, a compact algebraic descriptor of combinatorial bifurcations. This barcode captures structural changes in a dynamical system at the level of Morse decompositions and provides a characterization of the nature of observed transitions in terms of the Conley index. The construction of the Conley–Morse persistence barcode builds upon ideas from topological persistence. Specifically, we consider a persistence module obtained from the Conley index of invariant sets indexed over a poset. Using gentle algebras, we prove that this module decomposes into simple intervals (bars) and compute them by adapting the zigzag persistence algorithm to our purpose.},
  author       = {Dey, Tamal K. and Lipiński, Michał and Soriano Trigueros, Manuel},
  issn         = {1615-3383},
  journal      = {Foundations of Computational Mathematics},
  keywords     = {Multivector field, Conley index, Morse decomposition, Bifurcation, Continuation, Zigzag persistence, Persistence barcode, Gentle algebra},
  publisher    = {Springer},
  title        = {{Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations}},
  doi          = {10.1007/s10208-026-09766-6},
  year         = {2026},
}

@article{23155,
  abstract     = {In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we
show that, for a wide range of parameters d1 ≤ d2, there exists a coupling of
G(n,d1) and G(n,d2) satisfying that G(n,d1) ⊆ G(n,d2) with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime.
Our contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for
generating unions of random edge-disjoint perfect matchings, and refined estimates of Gao’s bounds on the number of perfect matchings in random regular graphs. In addition, we make progress towards another conjecture of Isaev,
McKay, Southwell and Zhukovskii.},
  author       = {Hollom, Lawrence and Lichev, Lyuben and Mond, Adva and Portier, Julien and Wang, Yiting},
  issn         = {2168-8737},
  journal      = {Annals of Applied Probability},
  keywords     = {Random regular graphs, coupling, contiguity, total variation distance, decomposition},
  number       = {5},
  pages        = {4716--4738},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Monotonicity and decompositions of random regular graphs}},
  doi          = {10.1214/26-AAP2345},
  volume       = {36},
  year         = {2026},
}

@inproceedings{22622,
  abstract     = {Cooperative software verification aims at improving the effectiveness and efficiency of software verification by enabling multiple verification tools to work together. Existing cooperative verification schemes, however, typically require specialized interfaces or tight integration, limiting their practical applicability. In our International Conference on Software Engineering (ICSE) 2025 publication, we introduce dynamic program splitting – a novel approach that enables cooperation between off-the-shelf verification tools without requiring any modifications. The key idea is to probe verification tools on a given verification task under a time limit and split tasks dynamically that cannot be verified under the given time constraints. The process continues recursively, incrementally identifying program parts that are particularly hard for the given verifier. The remaining unverified parts are provided to a second verifier, allowing to leverage the complementary strengths of different tools. Our evaluation on SV-COMP benchmarks demonstrates that cooperation through dynamic program splitting enables the verification of tasks that none of the individual verifiers can solve on their own.},
  author       = {Richter, Cedric and Chalupa, Marek and Jakobs, Marie Christine and Wehrheim, Heike},
  booktitle    = {Software Engineering 2026},
  issn         = {1617-5468},
  keywords     = {Software Verification, Cooperation, Program Decomposition},
  location     = {Bonn, Switzerland},
  pages        = {41--42},
  publisher    = {Gesellschaft für Informatik},
  title        = {{Off-the-Shelf cooperative software verification by splitting programs dynamically}},
  doi          = {10.18420/se2026_45},
  volume       = {P-377},
  year         = {2026},
}

@inproceedings{8287,
  abstract     = {Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.},
  author       = {Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian},
  booktitle    = {Proceedings of the International Conference on Embedded Software},
  keywords     = {reachability, hybrid systems, decomposition},
  location     = {Virtual },
  title        = {{Reachability analysis of linear hybrid systems via block decomposition}},
  year         = {2020},
}

@inproceedings{4097,
  abstract     = {Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.},
  author       = {Edelsbrunner, Herbert and Guibas, Leonidas and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha},
  booktitle    = {15th International Colloquium on Automata, Languages and Programming},
  isbn         = {978-3-540-19488-0},
  keywords     = {line segment, computational geometry, Jordan curve, cell decomposition, vertical tangency},
  location     = {Tampere, Finland},
  pages        = {214 -- 229},
  publisher    = {Springer},
  title        = {{Arrangements of curves in the plane - topology, combinatorics, and algorithms}},
  doi          = {10.1007/3-540-19488-6_118},
  volume       = {317},
  year         = {1988},
}