Georg Weissenbacher
Univ.Prof. Dipl.-Ing. / D.Phil.
Research Focus
- Computer Engineering: 30%
- Logic and Computation: 70%
About
Automated Software Verification
Roles
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Full Professor
Formal Methods in Systems Engineering, E192-04 -
Curriculum Commission for Computer Engineering
Principal Member
Courses
2024W
- Bachelor Thesis / 184.695 / PR
- Doctoral & Master Students Seminar / 181.224 / SE
- Introduction to Logical Methods in Computer Science / 184.766 / VO
- Research Seminar LogiCS / 184.767 / SE
- Scientific Research and Writing / 193.052 / SE
2025S
- Doctoral & Master Students Seminar / 181.224 / SE
- Introduction to Logical Methods in Computer Science / 184.766 / VO
- Program and System Verification / 184.741 / VU
- Research Seminar LogiCS / 184.767 / SE
- Seminar Formal Methods / 181.221 / SE
Projects
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AutoTest
2020 – 2021 / Vienna Science and Technology Fund (WWTF) -
LogiCs-Scholarships
2017 – 2025 / LCS
Publications: 188020 / 190648 / 192587 / 198885 -
Bit-level Accurate Reasoning and Interpolation
2016 – 2020 / Microsoft Research Limited
Publications: 56283 / 57273 -
Tools for Concurrent and distributed Systems
2011 – 2019 / Austrian Science Fund (FWF)
Publication: 53696
Publications
2024
- Distillation based Robustness Verification with PAC Guarantees / Indri, P., Blohm, P., Athavale, A., Bartocci, E., Weissenbacher, G., Maffei, M., Nickovic, D., Gärtner, T., & Malhotra, S. (2024). Distillation based Robustness Verification with PAC Guarantees. In Volume 235: International Conference on Machine Learning, 21-27 July 2024, Vienna, Austria. 41st International Conference on Machine Learning (ICML 2024), Vienna, Austria.
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Finding counterexamples to ∀∃ hyperproperties
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Nießen, T., & Weissenbacher, G. (2024, January 16). Finding counterexamples to ∀∃ hyperproperties [Conference Presentation]. Formal Methods for Incorrectness 2024, London, United Kingdom of Great Britain and Northern Ireland (the). https://doi.org/10.34726/5455
Download: Extended abstract (432 KB) -
Verifying Global Two-Safety Properties in Neural Networks with Confidence
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Athavale, A., Bartocci, E., Christakis, M., Maffei, M., Ničković, D., & Weissenbacher, G. (2024). Verifying Global Two-Safety Properties in Neural Networks with Confidence. In A. Gurfinkel & V. Ganesh (Eds.), Computer Aided Verification (pp. 329–351). Springer. https://doi.org/10.1007/978-3-031-65630-9_17
Projects: Browsec (2018–2024) / ForSmart (2023–2027) / ProbInG (2020–2025) / SFB SPyCoDe (2023–2026) / TAIGER (2023–2027)
2023
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A Formalization of Heisenbugs and Their Causes
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Sallinger, S., Weissenbacher, G., & Zuleger, F. (2023). A Formalization of Heisenbugs and Their Causes. In C. Ferreira & T. A. C. Willemse (Eds.), Software Engineering and Formal Methods : 21st International Conference, SEFM 2023, Eindhoven, The Netherlands, November 6-10, 2023, Proceedings (pp. 282–300). Springer. https://doi.org/10.34726/5381
Download: Preprint for self-archivation (552 KB)
Project: ARTIST (2021–2026)
2021
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Model Checking AUTOSAR Components with CBMC
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Durand, T., Fazekas, K., Weissenbacher, G., & Zwirchmayr, J. (2021). Model Checking AUTOSAR Components with CBMC. In Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021 (pp. 96–101). TU Wien Academic Press. https://doi.org/10.34727/2021/isbn.978-3-85448-046-4_18
Download: PDF (206 KB) - Bounded Model Checking of Speculative Non-Interference / Pescosta, E., Weissenbacher, G., & Zuleger, F. (2021). Bounded Model Checking of Speculative Non-Interference. In 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD). 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD), München, Germany. IEEE. https://doi.org/10.1109/iccad51958.2021.9643462
- Preface of the special issue on the conference on computer-aided verification 2018 / Chockler, H., & Weissenbacher, G. (2021). Preface of the special issue on the conference on computer-aided verification 2018. Formal Methods in System Design. https://doi.org/10.1007/s10703-021-00365-5
- Mutation testing with hyperproperties / Fellner, A., Tabaei Befrouei, M., & Weissenbacher, G. (2021). Mutation testing with hyperproperties. Software and Systems Modeling, 20(2), 405–427. https://doi.org/10.1007/s10270-020-00850-1
- Rely-guarantee bound analysis of parameterized concurrent shared-memory programs / Pani, T., Weissenbacher, G., & Zuleger, F. (2021). Rely-guarantee bound analysis of parameterized concurrent shared-memory programs. Formal Methods in System Design, 57(2), 270–302. https://doi.org/10.1007/s10703-021-00370-8
2020
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Thread-modular Counter Abstraction for Parameterized Program Safety
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Pani, T., Weissenbacher, G., & Zuleger, F. (2020). Thread-modular Counter Abstraction for Parameterized Program Safety. In A. Ivrii & O. Strichman (Eds.), Proceedings of the 20th Conference on Formal Methods in Computer-Aided Design – FMCAD 2020 (pp. 67–76). TU Wien Academic Press. https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_13
Download: Published version (434 KB) - Language Inclusion for Finite Prime Event Structures / Fellner, A., Tarrach, T., & Weissenbacher, G. (2020). Language Inclusion for Finite Prime Event Structures. In Verification, Model Checking, and Abstract Interpretation 21st International Conference, VMCAI 2020, New Orleans, LA, USA, January 16–21, 2020, Proceedings (pp. 314–336). Springer. https://doi.org/10.1007/978-3-030-39322-9_15
- Thread-modular Counter Abstraction for Parameterized Program Safety / Pani, T., Weissenbacher, G., & Zuleger, F. (2020). Thread-modular Counter Abstraction for Parameterized Program Safety. In Formal Methods in Computer-Aided Design (pp. 67–76). TU Wien Academic Press / IEEE. https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_13
- Multi-linear Strategy Extraction for QBF Expansion Proofs via Local Soundness / Schlaipfer, M., Slivovsky, F., Weissenbacher, G., & Zuleger, F. (2020). Multi-linear Strategy Extraction for QBF Expansion Proofs via Local Soundness. In Theory and Applications of Satisfiability Testing – SAT 2020 (pp. 429–446). LNCS. https://doi.org/10.1007/978-3-030-51825-7_30
- RAT Elimination / Rebola Pardo, A., & Weissenbacher, G. (2020). RAT Elimination. In L. Kovacs & E. Albert (Eds.), EPiC Series in Computing. EasyChair. https://doi.org/10.29007/fccb
- Preface of the Special Issue on the Conference on Formal Methods in Computer-Aided Design 2017 / Stewart, D., & Weissenbacher, G. (2020). Preface of the Special Issue on the Conference on Formal Methods in Computer-Aided Design 2017. Formal Methods in System Design, 57(3), 303–304. https://doi.org/10.1007/s10703-020-00357-x
- Extracting safe thread schedules from incomplete model checking results / Metzler, P., Suri, N., & Weissenbacher, G. (2020). Extracting safe thread schedules from incomplete model checking results. International Journal on Software Tools for Technology Transfer, 22(5), 565–581. https://doi.org/10.1007/s10009-020-00575-y
2019
- Extracting Safe Thread Schedules from Incomplete Model Checking Results / Metzler, P., Suri, N., & Weissenbacher, G. (2019). Extracting Safe Thread Schedules from Incomplete Model Checking Results. In Model Checking Software (pp. 153–171). LNCS, Springer. https://doi.org/10.1007/978-3-030-30923-7_9
- Model-Based Diagnosis with Multiple Observations / Ignatiev, A., Morgado, A., Marques-Silva, J., & Weissenbacher, G. (2019). Model-Based Diagnosis with Multiple Observations. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence. IJCAI 2019 - 28th International Joint Conference on Artificial Intelligence, Macao, Macao. https://doi.org/10.24963/ijcai.2019/155
- Mutation Testing with Hyperproperties / Fellner, A., Befrouei, M. T., & Weissenbacher, G. (2019). Mutation Testing with Hyperproperties. In Software Engineering and Formal Methods (pp. 203–221). https://doi.org/10.1007/978-3-030-30446-1_11
- Model-based, Mutation-driven Test-case Generation Via Heuristic-guided Branching Search / Fellner, A., Krenn, W., Schlick, R., Tarrach, T., & Weissenbacher, G. (2019). Model-based, Mutation-driven Test-case Generation Via Heuristic-guided Branching Search. ACM Transactions on Embedded Computing Systems, 18(1), 1–28. https://doi.org/10.1145/3289256
2018
- Randomized testing of distributed systems with probabilistic guarantees / Ozkan, B. K., Majumdar, R., Niksic, F., Befrouei, M. T., & Weissenbacher, G. (2018). Randomized testing of distributed systems with probabilistic guarantees. Proceedings of the ACM on Programming Languages, 2(OOPSLA), 1–28. https://doi.org/10.1145/3276530
- A Counting Semantics for Monitoring LTL Specifications over Finite Traces / Bartocci, E., Bloem, R., Nickovic, D., & Roeck, F. (2018). A Counting Semantics for Monitoring LTL Specifications over Finite Traces. In H. Chockler & G. Weissenbacher (Eds.), Computer Aided Verification: 30th International Conference, CAV 2018 (pp. 547–564). Springer. https://doi.org/10.1007/978-3-319-96145-3_29
- Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes / Kong, H., Bartocci, E., & Henzinger, T. A. (2018). Reachable Set Over-Approximation for Nonlinear Systems Using Piecewise Barrier Tubes. In H. Chockler & G. Weissenbacher (Eds.), Computer Aided Verification: 30th International Conference, CAV 2018 (pp. 449–467). Springer. https://doi.org/10.1007/978-3-319-96145-3_24
- Rely-Guarantee Reasoning for Automated Bound Analysis of Lock-Free Algorithms / Pani, T., Weissenbacher, G., & Zuleger, F. (2018). Rely-Guarantee Reasoning for Automated Bound Analysis of Lock-Free Algorithms. In 2018 Formal Methods in Computer Aided Design (FMCAD). International Conference on Formal Methods in Computer-Aided Design (FMCAD), Portland, OR, USA, Non-EU. FMCAD Inc. https://doi.org/10.23919/fmcad.2018.8603020
- A Separation Logic with Data: Small Models and Automation / Pagel, J., Jovanovic, D., & Weissenbacher, G. (2018). A Separation Logic with Data: Small Models and Automation. In Automated Reasoning (pp. 455–471). LNCS. https://doi.org/10.1007/978-3-319-94205-6_30
- Foundations and Tools for the Static Analysis of Ethereum Smart Contracts / Gishchenko, I., Maffei, M., & Schneidewind, C. (2018). Foundations and Tools for the Static Analysis of Ethereum Smart Contracts. In G. Weissenbacher & H. Chockler (Eds.), Computer Aided Verification (pp. 51–78). Springer Open. https://doi.org/10.1007/978-3-319-96145-3_4
- Computer Aided Verification / Computer Aided Verification. (2018). In H. Chockler & G. Weissenbacher (Eds.), Lecture Notes in Computer Science. Springer. https://doi.org/10.1007/978-3-319-96142-2
- Computer Aided Verification / Computer Aided Verification. (2018). In H. Chockler & G. Weissenbacher (Eds.), Lecture Notes in Computer Science. Springer. https://doi.org/10.1007/978-3-319-96145-3
2017
- Dynamic Reductions for Model Checking Concurrent Software / Günther, H., Laarman, A., Sokolova, A., & Weissenbacher, G. (2017). Dynamic Reductions for Model Checking Concurrent Software. In Verification, Model Checking, and Abstract Interpretation 18th International Conference, VMCAI 2017, Paris, France, January 15–17, 2017, Proceedings (pp. 246–265). Springer. https://doi.org/10.1007/978-3-319-52234-0_14
- Preface of the Special Issue in Memoriam Helmut Veith / Gottlob, G., Henzinger, T. A., & Weissenbacher, G. (2017). Preface of the Special Issue in Memoriam Helmut Veith. Formal Methods in System Design, 51(2), 267–269. https://doi.org/10.1007/s10703-017-0307-6
- Interpolation-based Model Checking and IC3 / Weissenbacher, G. (2017). Interpolation-based Model Checking and IC3. Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, Znaim, Tschechien, EU. http://hdl.handle.net/20.500.12708/86685
- Proceedings of Formal Methods in Computer Aided Design, FMCAD 2017 / Stewart, D., & Weissenbacher, G. (Eds.). (2017). Proceedings of Formal Methods in Computer Aided Design, FMCAD 2017. FMCAD Inc. https://doi.org/10.15781/T2JS9HQ7C
- Model-based, mutation-driven test case generation via heuristic-guided branching search / Fellner, A., Krenn, W., Schlick, R., Tarrach, T., & Weissenbacher, G. (2017). Model-based, mutation-driven test case generation via heuristic-guided branching search. In Proceedings of the 15th ACM-IEEE International Conference on Formal Methods and Models for System Design. MEMOCODE 2017: the 15th ACM-IEEE International Conference on Formal Methods and Models for System Design, Vienna, Austria, EU. ACM. https://doi.org/10.1145/3127041.3127049
2016
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Abstraction and mining of traces to explain concurrency bugs
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Tabaei Befrouei, M., Wang, C., & Weissenbacher, G. (2016). Abstraction and mining of traces to explain concurrency bugs. Formal Methods in System Design. https://doi.org/10.1007/s10703-015-0240-5
Download: PDF (1.57 MB) -
Vienna Verification Tool: IC3 for Parallel Software
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Günther, H., Laarman, A., & Weissenbacher, G. (2016). Vienna Verification Tool: IC3 for Parallel Software. In M. Chechik & J.-F. Raskin (Eds.), Tools and Algorithms for the Construction and Analysis of Systems : 22nd International Conference, TACAS 2016, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2-8, 2016, Proceedings. Springer Berlin. https://doi.org/10.1007/978-3-662-49674-9_69
Download: PDF (173 KB) - Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs / Schlaipfer, M., & Weissenbacher, G. (2016). Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs. Journal of Automated Reasoning, 57(1), 3–36. https://doi.org/10.1007/s10817-016-9364-6
- Logical methods in automated hardware and software verification / Weissenbacher, G. (2016). Logical methods in automated hardware and software verification [Professorial Dissertation, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/158852
- Interpolation algorithms and their applications in model checking / Weissenbacher, G. (2016). Interpolation algorithms and their applications in model checking. Automata, Logic and Games, Singapore, Non-EU. http://hdl.handle.net/20.500.12708/86305
- Error Invariants for Concurrent Traces / Holzer, A., Schwartz-Narbonne, D., Tabaei Befrouei, M., Weissenbacher, G., & Wies, T. (2016). Error Invariants for Concurrent Traces. In FM 2016: Formal Methods (pp. 370–387). Lecture Notes in Computer Science/Springer. https://doi.org/10.1007/978-3-319-48989-6_23
2015
- Boolean Satisfiability Solvers and Their Applications in Model Checking / Vizel, Y., Weissenbacher, G., & Malik, S. (2015). Boolean Satisfiability Solvers and Their Applications in Model Checking. Proceedings of the IEEE, 103(11), 2021–2035. https://doi.org/10.1109/jproc.2015.2455034
- Under-approximating loops in C programs for fast counterexample detection / Lewis, M., Kroening, D., & Weissenbacher, G. (2015). Under-approximating loops in C programs for fast counterexample detection. Formal Methods in System Design, 47(1), 75–92. https://doi.org/10.1007/s10703-015-0228-1
- Explaining Heisenbugs / Weissenbacher, G. (2015). Explaining Heisenbugs. In E. Bartocci & R. Majumdar (Eds.), Runtime Verification (p. XV). Lecture Notes in Computer Science/Springer. http://hdl.handle.net/20.500.12708/56231
- Proving Safety with Trace Automata and Bounded Model Checking / Lewis, M., Kroening, D., & Weissenbacher, G. (2015). Proving Safety with Trace Automata and Bounded Model Checking. In FM 2015: Formal Methods (pp. 325–341). Lecture Notes in Computer Science/Springer. https://doi.org/10.1007/978-3-319-19249-9_21
2014
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Reduction of Resolution Refutations and Interpolants via Subsumption
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Bloem, R., Malik, S., Schlaipfer, M., & Weissenbacher, G. (2014). Reduction of Resolution Refutations and Interpolants via Subsumption. In E. Yahav (Ed.), Hardware and Software: Verification and Testing : 10th International Haifa Verification Conference, HVC 2014, Haifa, Israel, November 18-20, 2014, Proceedings. Springer Cham. https://doi.org/10.1007/978-3-319-13338-6_15
Download: PDF (408 KB) - Counterexample to Induction-Guided Abstraction-Refinement (CTIGAR) / Birgmeier, J., Bradley, A. R., & Weissenbacher, G. (2014). Counterexample to Induction-Guided Abstraction-Refinement (CTIGAR). In Computer Aided Verification (pp. 831–848). Springer / LNCS. https://doi.org/10.1007/978-3-319-08867-9_55
- Incremental bounded software model checking / Günther, H., & Weissenbacher, G. (2014). Incremental bounded software model checking. In Proceedings of the 2014 International SPIN Symposium on Model Checking of Software. International SPIN Symposium on Model Checking of Software (SPIN), Stony Brook, NY, USA, Non-EU. ACM New York, NY, USA. https://doi.org/10.1145/2632362.2632374
- Abstraction and Mining of Traces to Explain Concurrency Bugs / Tabaei Befrouei, M., Wang, C., & Weissenbacher, G. (2014). Abstraction and Mining of Traces to Explain Concurrency Bugs. In Runtime Verification (pp. 162–177). Springer / LNCS. https://doi.org/10.1007/978-3-319-11164-3_14
- Silicon fault diagnosis using sequence interpolation with backbones / Zhu, C. S., Weissenbacher, G., & Malik, S. (2014). Silicon fault diagnosis using sequence interpolation with backbones. In ICCAD (pp. 348–355). IEEE Press Piscataway, NJ, USA. http://hdl.handle.net/20.500.12708/55310
2013
- Advanced SAT Techniques for Abstract Argumentation / Wallner, J. P., Weissenbacher, G., & Woltran, S. (2013). Advanced SAT Techniques for Abstract Argumentation. In Computational Logic in Multi-Agent Systems 14th International Workshop, CLIMA XIV, Corunna, Spain, September 16-18, 2013, Proceedings (pp. 138–154). Springer / LNCS. https://doi.org/10.1007/978-3-642-40624-9_9
- Under-Approximating Loops in C Programs for Fast Counterexample Detection / Kroening, D., Lewis, M., & Weissenbacher, G. (2013). Under-Approximating Loops in C Programs for Fast Counterexample Detection. In Computer Aided Verification (pp. 381–396). Springer / LNCS. https://doi.org/10.1007/978-3-642-39799-8_26
2012
- Labelled Interpolation Systems / Weissenbacher, G. (2012). Labelled Interpolation Systems. Dagstuhl Seminar 12461: Games and Decisions for Rigorous Systems Engineering, Dagstuhl, Deutschland, EU. http://hdl.handle.net/20.500.12708/85433
- Interpolant Strength Revisited / Weissenbacher, G. (2012). Interpolant Strength Revisited. In Theory and Applications of Satisfiability Testing – SAT 2012 (pp. 312–326). LNCS / Springer. https://doi.org/10.1007/978-3-642-31612-8_24
- Coverage-Based Trace Signal Selection for Fault Localisation in Post-silicon Validation / Charlie Shucheng, Z., Weissenbacher, G., & Malik, S. (2012). Coverage-Based Trace Signal Selection for Fault Localisation in Post-silicon Validation. In Hardware and Software: Verification and Testing (pp. 132–147). Lecture Notes in Computer Science. Springer Verlag. https://doi.org/10.1007/978-3-642-39611-3_16
- Parallel Assertions for Architectures with Weak Memory Models / Schwartz-Narbonne, D., Weissenbacher, G., & Malik, S. (2012). Parallel Assertions for Architectures with Weak Memory Models. In Automated Technology for Verification and Analysis (pp. 254–268). Lecture Notes in Computer Science. Springer Verlag. https://doi.org/10.1007/978-3-642-33386-6_21
Supervisions
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Consistency-based Software Fault Localization with Multiple Observations
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Graussam, L. (2024). Consistency-based Software Fault Localization with Multiple Observations [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2024.109000
Download: PDF (964 KB) -
Towards Automating Induction for Software Verification - Guiding Inductive Reasoning in Superposition-based Theorem Proving
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Georgiou, P. (2024). Towards Automating Induction for Software Verification - Guiding Inductive Reasoning in Superposition-based Theorem Proving [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2024.123801
Download: PDF (1.4 MB) -
Interference-based proofs in SAT solving
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Rebola-Pardo, A. (2021). Interference-based proofs in SAT solving [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2022.102507
Download: PDF (2.86 MB) -
Starkes modellbasiertes Mutationstesten
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Fellner, A. (2021). Starkes modellbasiertes Mutationstesten [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2021.88481
Download: PDF (1.68 MB) -
SpecBMC : bounded model checker for speculative non-interference
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Pescosta, E. (2020). SpecBMC : bounded model checker for speculative non-interference [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.76820
Download: PDF (1.89 MB) -
Eine Entscheidungsprozedur für Separation-Logic mit Daten
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Krulj, S. (2020). Eine Entscheidungsprozedur für Separation-Logic mit Daten [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.59461
Download: PDF (3.11 MB) -
Verifying automotive software components using C model checkers
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Durand, T. (2020). Verifying automotive software components using C model checkers [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.77681
Download: PDF (1.36 MB) -
A Tiny tweak to proof generation in miniSat-based SAT solvers & a complete and efficient DRAT proof checker
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Altmanninger, J. (2019). A Tiny tweak to proof generation in miniSat-based SAT solvers & a complete and efficient DRAT proof checker [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2019.62440
Download: PDF (3.44 MB) -
Angriffe gegen Neuronale Netzwerke
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Matak, M. (2019). Angriffe gegen Neuronale Netzwerke [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2019.61021
Download: PDF (5.07 MB) -
Effective error explanation techniques for concurrent software
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Tabaei Befrouei, M. (2016). Effective error explanation techniques for concurrent software [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2016.40440
Download: PDF (1.8 MB) -
Complexity results and algorithms for argumentation : Dung's frameworks and beyond
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Wallner, J. (2014). Complexity results and algorithms for argumentation : Dung’s frameworks and beyond [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2014.24438
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Software verification with IC3 via abstraction and interpolation
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Birgmeier, J. (2013). Software verification with IC3 via abstraction and interpolation [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2013.22441
Download: PDF (1010 KB)