@inproceedings{7411,
  abstract     = {Proofs of sequential work (PoSW) are proof systems where a prover, upon receiving a statement χ and a time parameter T computes a proof ϕ(χ,T) which is efficiently and publicly verifiable. The proof can be computed in T sequential steps, but not much less, even by a malicious party having large parallelism. A PoSW thus serves as a proof that T units of time have passed since χ

was received.

PoSW were introduced by Mahmoody, Moran and Vadhan [MMV11], a simple and practical construction was only recently proposed by Cohen and Pietrzak [CP18].

In this work we construct a new simple PoSW in the random permutation model which is almost as simple and efficient as [CP18] but conceptually very different. Whereas the structure underlying [CP18] is a hash tree, our construction is based on skip lists and has the interesting property that computing the PoSW is a reversible computation.
The fact that the construction is reversible can potentially be used for new applications like constructing proofs of replication. We also show how to “embed” the sloth function of Lenstra and Weselowski [LW17] into our PoSW to get a PoSW where one additionally can verify correctness of the output much more efficiently than recomputing it (though recent constructions of “verifiable delay functions” subsume most of the applications this construction was aiming at).},
  author       = {Abusalah, Hamza M and Kamath Hosdurg, Chethan and Klein, Karen and Pietrzak, Krzysztof Z and Walter, Michael},
  booktitle    = {Advances in Cryptology – EUROCRYPT 2019},
  isbn         = {9783030176556},
  issn         = {1611-3349},
  location     = {Darmstadt, Germany},
  pages        = {277--291},
  publisher    = {Springer International Publishing},
  title        = {{Reversible proofs of sequential work}},
  doi          = {10.1007/978-3-030-17656-3_10},
  volume       = {11477},
  year         = {2019},
}

@inproceedings{6163,
  abstract     = {We propose a new non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. Every grid point, each represented by integer 3-coordinates, corresponds to rhombic dodecahedron centroid. Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. A characterization of a 3D digital sphere with relevant topological features is proposed as well with the help of a 48 symmetry that comes with the new coordinate system.},
  author       = {Biswas, Ranita and Largeteau-Skapin, Gaëlle and Zrour, Rita and Andres, Eric},
  booktitle    = {21st IAPR International Conference on Discrete Geometry for Computer Imagery},
  isbn         = {978-3-6624-6446-5},
  issn         = {0302-9743},
  location     = {Marne-la-Vallée, France},
  pages        = {27--37},
  publisher    = {Springer Berlin Heidelberg},
  title        = {{Rhombic dodecahedron grid—coordinate system and 3D digital object definitions}},
  doi          = {10.1007/978-3-030-14085-4_3},
  volume       = {11414},
  year         = {2019},
}

@inproceedings{6462,
  abstract     = {A controller is a device that interacts with a plant. At each time point,it reads the plant’s state and issues commands with the goal that the plant oper-ates optimally. Constructing optimal controllers is a fundamental and challengingproblem. Machine learning techniques have recently been successfully applied totrain controllers, yet they have limitations. Learned controllers are monolithic andhard to reason about. In particular, it is difficult to add features without retraining,to guarantee any level of performance, and to achieve acceptable performancewhen encountering untrained scenarios. These limitations can be addressed bydeploying quantitative run-timeshieldsthat serve as a proxy for the controller.At each time point, the shield reads the command issued by the controller andmay choose to alter it before passing it on to the plant. We show how optimalshields that interfere as little as possible while guaranteeing a desired level ofcontroller performance, can be generated systematically and automatically usingreactive  synthesis.  First,  we  abstract  the  plant  by  building  a  stochastic  model.Second, we consider the learned controller to be a black box. Third, we mea-surecontroller performanceandshield interferenceby two quantitative run-timemeasures that are formally defined using weighted automata. Then, the problemof constructing a shield that guarantees maximal performance with minimal inter-ference is the problem of finding an optimal strategy in a stochastic2-player game“controller versus shield” played on the abstract state space of the plant with aquantitative objective obtained from combining the performance and interferencemeasures. We illustrate the effectiveness of our approach by automatically con-structing lightweight shields for learned traffic-light controllers in various roadnetworks. The shields we generate avoid liveness bugs, improve controller per-formance in untrained and changing traffic situations, and add features to learnedcontrollers, such as giving priority to emergency vehicles.},
  author       = {Avni, Guy and Bloem, Roderick and Chatterjee, Krishnendu and Henzinger, Thomas A and Konighofer, Bettina and Pranger, Stefan},
  booktitle    = {31st International Conference on Computer-Aided Verification},
  isbn         = {9783030255398},
  issn         = {0302-9743},
  location     = {New York, NY, United States},
  pages        = {630--649},
  publisher    = {Springer},
  title        = {{Run-time optimization for learned controllers through quantitative games}},
  doi          = {10.1007/978-3-030-25540-4_36},
  volume       = {11561},
  year         = {2019},
}

@inproceedings{6482,
  abstract     = {Computer vision systems for automatic image categorization have become accurate and reliable enough that they can run continuously for days or even years as components of real-world commercial applications. A major open problem in this context, however, is quality control. Good classification performance can only be expected if systems run under the specific conditions, in particular data distributions, that they were trained for. Surprisingly, none of the currently used deep network architectures have a built-in functionality that could detect if a network operates on data from a distribution it was not trained for, such that potentially a warning to the human users could be triggered. In this work, we describe KS(conf), a procedure for detecting such outside of specifications (out-of-specs) operation, based on statistical testing of the network outputs. We show by extensive experiments using the ImageNet, AwA2 and DAVIS datasets on a variety of ConvNets architectures that KS(conf) reliably detects out-of-specs situations. It furthermore has a number of properties that make it a promising candidate for practical deployment: it is easy to implement, adds almost no overhead to the system, works with all networks, including pretrained ones, and requires no a priori knowledge of how the data distribution could change. },
  author       = {Sun, Rémy and Lampert, Christoph},
  isbn         = {9783030129385},
  issn         = {1611-3349},
  location     = {Stuttgart, Germany},
  pages        = {244--259},
  publisher    = {Springer Nature},
  title        = {{KS(conf): A light-weight test if a ConvNet operates outside of Its specifications}},
  doi          = {10.1007/978-3-030-12939-2_18},
  volume       = {11269},
  year         = {2019},
}

@inproceedings{6493,
  abstract     = {We present two algorithmic approaches for synthesizing linear hybrid automata from experimental data. Unlike previous approaches, our algorithms work without a template and generate an automaton with nondeterministic guards and invariants, and with an arbitrary number and topology of modes. They thus construct a succinct model from the data and provide formal guarantees. In particular, (1) the generated automaton can reproduce the data up to a specified tolerance and (2) the automaton is tight, given the first guarantee. Our first approach encodes the synthesis problem as a logical formula in the theory of linear arithmetic, which can then be solved by an SMT solver. This approach minimizes the number of modes in the resulting model but is only feasible for limited data sets. To address scalability, we propose a second approach that does not enforce to find a minimal model. The algorithm constructs an initial automaton and then iteratively extends the automaton based on processing new data. Therefore the algorithm is well-suited for online and synthesis-in-the-loop applications. The core of the algorithm is a membership query that checks whether, within the specified tolerance, a given data set can result from the execution of a given automaton. We solve this membership problem for linear hybrid automata by repeated reachability computations. We demonstrate the effectiveness of the algorithm on synthetic data sets and on cardiac-cell measurements.},
  author       = {Garcia Soto, Miriam and Henzinger, Thomas A and Schilling, Christian and Zeleznik, Luka},
  booktitle    = {31st International Conference on Computer-Aided Verification},
  isbn         = {9783030255398},
  issn         = {0302-9743},
  keywords     = {Synthesis, Linear hybrid automaton, Membership},
  location     = {New York City, NY, USA},
  pages        = {297--314},
  publisher    = {Springer},
  title        = {{Membership-based synthesis of linear hybrid automata}},
  doi          = {10.1007/978-3-030-25540-4_16},
  volume       = {11561},
  year         = {2019},
}

@inproceedings{8298,
  abstract     = {Sharding, or partitioning the system’s state so that different subsets of participants handle it, is a proven approach to building distributed systems whose total capacity scales horizontally with the number of participants. Many distributed ledgers have adopted this approach to increase their performance, however, they focus on the permissionless setting that assumes the existence of a strong adversary. In this paper, we deploy channels for permissioned blockchains. Our first contribution is to adapt sharding on asset-management applications for the permissioned setting, while preserving liveness and safety even on transactions spanning across-channels. Our second contribution is to leverage channels as a confidentiality boundary, enabling different organizations and consortia to preserve their privacy within their channels and still be part of a bigger collaborative ecosystem. To make our system concrete we map it on top of Hyperledger Fabric.},
  author       = {Androulaki, Elli and Cachin, Christian and De Caro, Angelo and Kokoris Kogias, Eleftherios},
  booktitle    = {Computer Security},
  isbn         = {9783319990729},
  issn         = {0302-9743},
  location     = {Barcelona, Spain},
  pages        = {111--131},
  publisher    = {Springer Nature},
  title        = {{Channels: Horizontal scaling and confidentiality on permissioned blockchains}},
  doi          = {10.1007/978-3-319-99073-6_6},
  volume       = {11098},
  year         = {2018},
}

@inproceedings{6941,
  abstract     = {Bitcoin has become the most successful cryptocurrency ever deployed, and its most distinctive feature is that it is decentralized. Its underlying protocol (Nakamoto consensus) achieves this by using proof of work, which has the drawback that it causes the consumption of vast amounts of energy to maintain the ledger. Moreover, Bitcoin mining dynamics have become less distributed over time.

Towards addressing these issues, we propose SpaceMint, a cryptocurrency based on proofs of space instead of proofs of work. Miners in SpaceMint dedicate disk space rather than computation. We argue that SpaceMint’s design solves or alleviates several of Bitcoin’s issues: most notably, its large energy consumption. SpaceMint also rewards smaller miners fairly according to their contribution to the network, thus incentivizing more distributed participation.

This paper adapts proof of space to enable its use in cryptocurrency, studies the attacks that can arise against a Bitcoin-like blockchain that uses proof of space, and proposes a new blockchain format and transaction types to address these attacks. Our prototype shows that initializing 1 TB for mining takes about a day (a one-off setup cost), and miners spend on average just a fraction of a second per block mined. Finally, we provide a game-theoretic analysis modeling SpaceMint as an extensive game (the canonical game-theoretic notion for games that take place over time) and show that this stylized game satisfies a strong equilibrium notion, thereby arguing for SpaceMint ’s stability and consensus.},
  author       = {Park, Sunoo and Kwon, Albert and Fuchsbauer, Georg and Gazi, Peter and Alwen, Joel F and Pietrzak, Krzysztof Z},
  booktitle    = {22nd International Conference on Financial Cryptography and Data Security},
  isbn         = {9783662583869},
  issn         = {1611-3349},
  location     = {Nieuwpoort, Curacao},
  pages        = {480--499},
  publisher    = {Springer Nature},
  title        = {{SpaceMint: A cryptocurrency based on proofs of space}},
  doi          = {10.1007/978-3-662-58387-6_26},
  volume       = {10957},
  year         = {2018},
}

@inproceedings{6164,
  abstract     = {In this paper, we propose an algorithm to build discrete spherical shell having integer center and real-valued inner and outer radii on the face-centered cubic (FCC) grid. We address the problem by mapping it to a 2D scenario and building the shell layer by layer on hexagonal grids with additive manufacturing in mind. The layered hexagonal grids get shifted according to need as we move from one layer to another and forms the FCC grid in 3D. However, we restrict our computation strictly to 2D in order to utilize symmetry and simplicity.},
  author       = {Koshti, Girish and Biswas, Ranita and Largeteau-Skapin, Gaëlle and Zrour, Rita and Andres, Eric and Bhowmick, Partha},
  booktitle    = {19th International Workshop},
  isbn         = {978-3-030-05287-4},
  issn         = {1611-3349},
  location     = {Porto, Portugal},
  pages        = {82--96},
  publisher    = {Springer},
  title        = {{Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D}},
  doi          = {10.1007/978-3-030-05288-1_7},
  volume       = {11255},
  year         = {2018},
}

@inproceedings{11772,
  abstract     = {A dynamic graph algorithm is a data structure that supports operations on dynamically changing graphs.},
  author       = {Henzinger, Monika H},
  booktitle    = {44th International Conference on Current Trends in Theory and Practice of Computer Science},
  isbn         = {9783319731162},
  issn         = {0302-9743},
  location     = {Krems, Austria},
  pages        = {40–44},
  publisher    = {Springer Nature},
  title        = {{The state of the art in dynamic graph algorithms}},
  doi          = {10.1007/978-3-319-73117-9_3},
  volume       = {10706},
  year         = {2017},
}

@inproceedings{5801,
  abstract     = {Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space.},
  author       = {Dwivedi, Shivam and Gupta, Aniket and Roy, Siddhant and Biswas, Ranita and Bhowmick, Partha},
  booktitle    = {20th IAPR International Conference},
  isbn         = {978-3-319-66271-8},
  issn         = {1611-3349},
  location     = {Vienna, Austria},
  pages        = {347--359},
  publisher    = {Springer Nature},
  title        = {{Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space}},
  doi          = {10.1007/978-3-319-66272-5_28},
  volume       = {10502},
  year         = {2017},
}

@inproceedings{5802,
  abstract     = {This papers introduces a definition of digital primitives based on focal points and weighted distances (with positive weights). The proposed definition is applicable to general dimensions and covers in its gamut various regular curves and surfaces like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids, Cartesian k-ovals, etc. Several interesting properties are presented for this class of digital primitives such as space partitioning, topological separation, and connectivity properties. To demonstrate further the potential of this new way of defining digital primitives, we propose, as extension, another class of digital conics defined by focus-directrix combination.},
  author       = {Andres, Eric and Biswas, Ranita and Bhowmick, Partha},
  booktitle    = {20th IAPR International Conference},
  isbn         = {978-3-319-66271-8},
  issn         = {1611-3349},
  location     = {Vienna, Austria},
  pages        = {388--398},
  publisher    = {Springer Nature},
  title        = {{Digital primitives defined by weighted focal set}},
  doi          = {10.1007/978-3-319-66272-5_31},
  volume       = {10502},
  year         = {2017},
}

@inbook{5803,
  abstract     = {Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.},
  author       = {Biswas, Ranita and Bhowmick, Partha},
  booktitle    = {Combinatorial image analysis},
  isbn         = {978-3-319-59107-0},
  issn         = {0302-9743},
  location     = {Plovdiv, Bulgaria},
  pages        = {93--104},
  publisher    = {Springer Nature},
  title        = {{Construction of persistent Voronoi diagram on 3D digital plane}},
  doi          = {10.1007/978-3-319-59108-7_8},
  volume       = {10256},
  year         = {2017},
}

@inbook{625,
  abstract     = {In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision problems for classical quantitative objectives, such as sum, discounted sum, energy, and mean-payoff for two standard models of reactive systems, namely, graphs and graph games.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A},
  booktitle    = {Models, Algorithms, Logics and Tools},
  editor       = {Aceto, Luca and Bacci, Giorgio and Ingólfsdóttir, Anna and Legay, Axel and Mardare, Radu},
  isbn         = {978-3-319-63120-2},
  issn         = {0302-9743},
  pages        = {367 -- 381},
  publisher    = {Springer},
  title        = {{The cost of exactness in quantitative reachability}},
  doi          = {10.1007/978-3-319-63121-9_18},
  volume       = {10460},
  year         = {2017},
}

@proceedings{638,
  abstract     = {This book constitutes the refereed proceedings of the 9th InternationalWorkshop on Numerical Software Verification, NSV 2016, held in Toronto, ON, Canada in July 2011 - colocated with CAV 2016, the 28th International Conference on Computer Aided Verification.
The NSV workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.},
  editor       = {Bogomolov, Sergiy and Martel, Matthieu and Prabhakar, Pavithra},
  issn         = {0302-9743},
  location     = {Toronto, ON, Canada},
  publisher    = {Springer},
  title        = {{Numerical Software Verification}},
  doi          = {10.1007/978-3-319-54292-8},
  volume       = {10152},
  year         = {2017},
}

@inproceedings{13160,
  abstract     = {Transforming deterministic ω
-automata into deterministic parity automata is traditionally done using variants of appearance records. We present a more efficient variant of this approach, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and find out that our method produces smaller automata than previous approaches. Moreover, the experiments demonstrate the potential of our method for LTL synthesis, using LTL-to-Rabin translators. It leads to significantly smaller parity automata when compared to state-of-the-art approaches on complex formulae.},
  author       = {Kretinsky, Jan and Meggendorfer, Tobias and Waldmann, Clara and Weininger, Maximilian},
  booktitle    = {Tools and Algorithms for the Construction and Analysis of Systems},
  isbn         = {9783662545768},
  issn         = {1611-3349},
  location     = {Uppsala, Sweden},
  pages        = {443--460},
  publisher    = {Springer},
  title        = {{Index appearance record for transforming Rabin automata into parity automata}},
  doi          = {10.1007/978-3-662-54577-5_26},
  volume       = {10205},
  year         = {2017},
}

@inproceedings{12571,
  abstract     = {We consider the problems of maintaining approximate maximum matching and minimum vertex cover in a dynamic graph. Starting with the seminal work of Onak and Rubinfeld [STOC 2010], this problem has received significant attention in recent years. Very recently, extending the framework of Baswana, Gupta and Sen [FOCS 2011], Solomon [FOCS 2016] gave a randomized 2-approximation dynamic algorithm for this problem that has amortized update time of O(1) with high probability. We consider the natural open question of derandomizing this result. We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1). Previously, the best deterministic algorithm for this problem was due to Bhattacharya, Henzinger and Italiano [SODA 2015]; it had an approximation ratio of (2+ϵ) and an amortized update time of O(logn/ϵ2). Our result can be generalized to give a fully dynamic O(f3)-approximation algorithm with O(f2) amortized update time for the hypergraph vertex cover and fractional matching problems, where every hyperedge has at most f vertices.},
  author       = {Bhattacharya, Sayan and Chakrabarty, Deeparnab and Henzinger, Monika H},
  booktitle    = {19th International Conference on Integer Programming and Combinatorial Optimization},
  isbn         = {9783319592497},
  issn         = {0302-9743},
  location     = {Waterloo, ON, Canada},
  pages        = {86--98},
  publisher    = {Springer Nature},
  title        = {{Deterministic fully dynamic approximate vertex cover and fractional matching in O(1) amortized update time}},
  doi          = {10.1007/978-3-319-59250-3_8},
  volume       = {10328},
  year         = {2017},
}

@inbook{1094,
  abstract     = {Immunogold labeling of freeze-fracture replicas has recently been used for high-resolution visualization of protein localization in electron microscopy. This method has higher labeling efficiency than conventional immunogold methods for membrane molecules allowing precise quantitative measurements. However, one of the limitations of freeze-fracture replica immunolabeling is difficulty in keeping structural orientation and identifying labeled profiles in complex tissues like brain. The difficulty is partly due to fragmentation of freeze-fracture replica preparations during labeling procedures and limited morphological clues on the replica surface. To overcome these issues, we introduce here a grid-glued replica method combined with SEM observation. This method allows histological staining before dissolving the tissue and easy handling of replicas during immunogold labeling, and keeps the whole replica surface intact without fragmentation. The procedure described here is also useful for matched double-replica analysis allowing further identification of labeled profiles in corresponding P-face and E-face.},
  author       = {Harada, Harumi and Shigemoto, Ryuichi},
  booktitle    = {High-Resolution Imaging of Cellular Proteins},
  issn         = {1611-3349},
  pages        = {203 -- 216},
  publisher    = {Springer},
  title        = {{Immunogold protein localization on grid-glued freeze-fracture replicas}},
  doi          = {10.1007/978-1-4939-6352-2_12},
  volume       = {1474},
  year         = {2016},
}

@inbook{5805,
  abstract     = {Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy.},
  author       = {Sen, Nabhasmita and Biswas, Ranita and Bhowmick, Partha},
  booktitle    = {Computational Topology in Image Context},
  isbn         = {978-3-319-39440-4},
  issn         = {1611-3349},
  location     = {Marseille, France},
  pages        = {253--264},
  publisher    = {Springer Nature},
  title        = {{On some local topological properties of naive discrete sphere}},
  doi          = {10.1007/978-3-319-39441-1_23},
  volume       = {9667},
  year         = {2016},
}

@inproceedings{5806,
  abstract     = {Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane.},
  author       = {Biswas, Ranita and Bhowmick, Partha},
  booktitle    = {Discrete Geometry for Computer Imagery},
  isbn         = {978-3-319-32359-6},
  issn         = {0302-9743},
  location     = {Nantes, France},
  pages        = {256--267},
  publisher    = {Springer Nature},
  title        = {{On functionality of quadraginta octants of naive sphere with application to circle drawing}},
  doi          = {10.1007/978-3-319-32360-2_20},
  volume       = {9647},
  year         = {2016},
}

@inbook{5809,
  abstract     = {A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.},
  author       = {Biswas, Ranita and Bhowmick, Partha and Brimkov, Valentin E.},
  booktitle    = {Combinatorial image analysis},
  isbn         = {978-3-319-26144-7},
  issn         = {1611-3349},
  location     = {Kolkata, India},
  pages        = {86--100},
  publisher    = {Springer Nature},
  title        = {{On the connectivity and smoothness of discrete spherical circles}},
  doi          = {10.1007/978-3-319-26145-4_7},
  volume       = {9448},
  year         = {2016},
}

