PPL swMATH ID: 5357 Software Authors: Bagnara, Roberto; Ricci, Elisa; Zaffanella, Enea; Hill, Patricia M. Description: Possibly not closed convex polyhedra and the Parma Polyhedra Library. The domain of convex polyhedra is employed in several systems for the analysis and verification of hardware and software components. Current applications span imperative, functional and logic languages, synchronous languages and synchronization protocols, real-time and hybrid systems. Since the seminal work of P. Cousot and N. Halbwachs, convex polyhedra have thus played an important role in the formal methods community and several critical tasks rely on their software implementations. Despite this, existing libraries for the manipulation of convex polyhedra are still research prototypes and suffer from limitations that make their usage problematic, especially in critical applications. Furthermore, there is inadequate support for polyhedra that are Not Necessarily Closed (NNC), i.e., polyhedra that are described by systems of constraints where strict inequalities are allowed to occur. This paper presents the Parma Polyhedra Library, a new, robust and complete implementation of NNC convex polyhedra, concentrating on the distinctive features of the library and on the novel theoretical underpinnings. Homepage: http://bugseng.com/products/ppl Programming Languages: C++ Related Software: HyTech; Apron; PHAVer; Uppaal; ASTREE; polymake; PolyLib; SageMath; SpaceEx; GitHub; z3; gmp; Yices; IMITATOR; SCIP; lrs; Dagger; InvGen; Kronos; Gurobi Cited in: 118 Documents Further Publications: http://bugseng.com/products/ppl/documentation/bibliography Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Possibly not closed convex polyhedra and the Parma Polyhedra Library. Zbl 1015.68215Bagnara, Roberto; Ricci, Elisa; Zaffanella, Enea; Hill, Patricia M. 2002 all top 5 Cited by 219 Authors 12 Zaffanella, Enea 8 Gallagher, John P. 7 André, Étienne 7 Bagnara, Roberto 5 Hill, Patricia M. 5 Kafle, Bishoksan 5 Sankaranarayanan, Sriram 4 Amato, Gianluca 4 Genaim, Samir 4 Monniaux, David P. 3 Eifler, Leon 3 Frehse, Goran 3 Gleixner, Ambros M. 3 Halbwachs, Nicolas 3 Joswig, Michael 3 Kwiatkowska, Marta Z. 3 Larsen, Kim Guldstrand 3 Petrucci, Laure 3 Scozzari, Francesca 2 Albert, Elvira 2 Allamigeon, Xavier 2 Arenas, Puri 2 Azgomi, Mohammad Abdollahi 2 Banda, Gourinath 2 Barnat, Jiří 2 Basset, Nicolas 2 Becchi, Anna 2 Ben-Amram, Amir M. 2 Benerecetti, Massimo 2 Beneš, Nikola 2 Bezděk, Peter 2 Černá, Ivana 2 Cortesi, Agostino 2 Dang, Thao 2 De Angelis, Emanuele 2 Doyen, Laurent 2 Faella, Marco 2 Fioravanti, Fabio 2 Fribourg, Laurent 2 Gange, Graeme 2 Ganty, Pierre 2 Gupta, Aarti 2 Ivančić, Franjo 2 Jovanović, Aleksandra Ž. 2 Katz, Ricardo David 2 Köppe, Matthias 2 Mambakam, Akshay 2 Maréchal, Alexandre 2 Merchat, David 2 Motallebi, Hassan 2 Parton, Maurizio 2 Payet, Étienne 2 Périn, Michael 2 Pettorossi, Alberto 2 Prabhakar, Pavithra 2 Proietti, Maurizio 2 Puebla, Germán 2 Raskin, Jean-François 2 Rodríguez, Margarita M. L. 2 Rybalchenko, Andrey 2 Schachte, Peter 2 Søndergaard, Harald 2 Soto, Miriam García 2 Spoto, Fausto 2 Strub, Pierre-Yves 2 Stuckey, Peter James 2 Sun, Jun 2 van de Pol, Jan Cornelis 2 Vicente-Pérez, José 2 Zhou, Yuan 1 Ábrahám, Erika 1 Althoff, Matthias 1 Arceri, Vincenzo 1 Asarin, Eugene 1 Assarf, Benjamin 1 Avis, David M. 1 Bakhirkin, Alexey 1 Bastrakov, Sergeĭ Ivanovich 1 Basu, Amitabh 1 Batkhin, Alexandr B. 1 Batt, Grégory 1 Becker, Stephen R. 1 Ben Sassi, Mohamed Amin 1 Boutonnet, Rémy 1 Brim, Luboš 1 Bruno, Alexander Dmitrievich 1 Chaki, Sagar 1 Cimatti, Alessandro 1 Cohen, Albert 1 Colón, Michael A. 1 Coquard, Emmanuel 1 Di Summa, Marco 1 Dluhoš, P. 1 Doménech, Jesús J. 1 Dong, JinSong 1 Ebert, Tristan 1 Fages, François 1 Fahrenberg, Uli 1 Fajardo, María D. 1 Ferrara, Pietro ...and 119 more Authors all top 5 Cited in 30 Serials 8 Theoretical Computer Science 7 Formal Methods in System Design 6 Information and Computation 6 Theory and Practice of Logic Programming 3 Mathematical Programming Computation 2 Journal of Symbolic Computation 2 Discrete Event Dynamic Systems 2 Mathematical Programming. Series A. Series B 2 Higher-Order and Symbolic Computation 2 Logical Methods in Computer Science 1 ACM Transactions on Mathematical Software 1 Journal of Optimization Theory and Applications 1 Programming and Computer Software 1 Journal of Automated Reasoning 1 SIAM Journal on Discrete Mathematics 1 Real-Time Systems 1 Computational Geometry 1 Applicable Algebra in Engineering, Communication and Computing 1 Computational and Applied Mathematics 1 Constraints 1 European Journal of Control 1 Journal of the ACM 1 Fundamenta Informaticae 1 The Journal of Logic and Algebraic Programming 1 Computer Languages, Systems & Structures 1 Mathematics in Computer Science 1 Nonlinear Analysis. Hybrid Systems 1 Journal of Logical and Algebraic Methods in Programming 1 EURO Advanced Tutorials on Operational Research 1 Discrete Mathematics and its Applications all top 5 Cited in 21 Fields 95 Computer science (68-XX) 22 Operations research, mathematical programming (90-XX) 17 Convex and discrete geometry (52-XX) 15 Systems theory; control (93-XX) 11 Mathematical logic and foundations (03-XX) 10 Numerical analysis (65-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Combinatorics (05-XX) 4 Algebraic geometry (14-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) Citations by Year