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Werner Damm
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- affiliation: University of Oldenburg, Germany
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2020 – today
- 2020
- [c77]Birte Kramer
, Christian Neurohr
, Matthias Büker, Eckard Böde, Martin Fränzle
, Werner Damm:
Identification and Quantification of Hazardous Scenarios for Automated Driving. IMBSA 2020: 163-178
2010 – 2019
- 2019
- [c76]Werner Damm, Günter Ehmen, Kim Grüttner, Philipp Ittershagen, Björn Koopmann
, Frank Poppen, Ingo Stierand:
Multi-layer time coherency in the development of ADAS/AD systems: design approach and tooling. DESTION@CPSIoTWeek 2019: 20-30 - [c75]Werner Damm, Martin Fränzle, Andreas Lüdtke
, Jochem W. Rieger
, Alexander Trende
, Anirudh Unni:
Integrating Neurophysiological Sensors and Driver Models for Safe and Performant Automated Vehicle Control in Mixed Traffic. IV 2019: 82-89 - [c74]Werner Damm, Martin Fränzle
, Willem Hagemann, Paul Kröger, Astrid Rakow:
Dynamic Conflict Resolution Using Justification Based Reasoning. CREST@ETAPS 2019: 47-65 - [i4]Werner Damm, Martin Fränzle, Andreas Lüdtke, Jochem W. Rieger, Alexander Trende, Anirudh Unni:
Integrating Neurophysiological Sensors and Driver Models for Safe and Performant Automated Vehicle Control in Mixed Traffic. CoRR abs/1902.04929 (2019) - [i3]Werner Damm, Martin Fränzle, Willem Hagemann, Paul Kröger, Astrid Rakow:
Justification Based Reasoning in Dynamic Conflict Resolution. CoRR abs/1905.11764 (2019) - 2018
- [j27]Albert Benveniste, Benoît Caillaud
, Dejan Nickovic, Roberto Passerone, Jean-Baptiste Raclet, Philipp Reinkemeier, Alberto L. Sangiovanni-Vincentelli, Werner Damm, Thomas A. Henzinger, Kim G. Larsen:
Contracts for System Design. Found. Trends Electron. Des. Autom. 12(2-3): 124-400 (2018) - [c73]Werner Damm, Martin Fränzle, Sebastian Gerwinn, Paul Kröger:
Perspectives on the Validation and Verification of Machine Learning Systems in the Context of Highly Automated Vehicles. AAAI Spring Symposia 2018 - [c72]Werner Damm, Eike Möhlmann
, Thomas Peikenkamp, Astrid Rakow:
A Formal Semantics for Traffic Sequence Charts. Principles of Modeling 2018: 182-205 - [c71]Werner Damm, Roland Galbas:
Exploiting Learning and Scenario-Based Specification Languages for the Verification and Validation of Highly Automated Driving. SEFAIAS@ICSE 2018: 39-46 - 2017
- [j26]Werner Damm, Ralf Kalmar:
Autonome Systeme - Fähigkeiten und Anforderungen. Inform. Spektrum 40(5): 400-408 (2017) - [j25]Ernst Althaus, Björn Beber, Werner Damm, Stefan Disch, Willem Hagemann, Astrid Rakow, Christoph Scholl, Uwe Waldmann, Boris Wirtz:
Verification of linear hybrid systems with large discrete state spaces using counterexample-guided abstraction refinement. Sci. Comput. Program. 148: 123-160 (2017) - 2016
- [c70]Werner Damm, Bernd Finkbeiner, Astrid Rakow:
What You Really Need To Know About Your Neighbor. SYNT@CAV 2016: 21-34 - [i2]Werner Damm, Matthias Horbach, Viorica Sofronie-Stokkermans:
Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata. CoRR abs/1601.01648 (2016) - 2015
- [c69]Werner Damm, Alberto L. Sangiovanni-Vincentelli:
A conceptual model of system of systems. SWEC@CPSWeek 2015: 19-27 - [c68]Werner Damm:
AVACS: Automatic Verification and Analysis of Complex Systems Highlights and Lessons Learned. FM 2015: 18-19 - [c67]Philipp Reinkemeier, Albert Benveniste, Werner Damm, Ingo Stierand:
Contracts for Schedulability Analysis. FORMATS 2015: 270-287 - [c66]Werner Damm, Matthias Horbach, Viorica Sofronie-Stokkermans:
Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata. FroCos 2015: 186-202 - 2014
- [c65]Werner Damm, Bernd Finkbeiner:
Automatic Compositional Synthesis of Distributed Systems. FM 2014: 179-193 - [c64]Werner Damm, Eike Möhlmann
, Astrid Rakow:
Component based design of hybrid systems: a case study on concurrency and coupling. HSCC 2014: 145-150 - [i1]Tetsuya Tohdo, Werner Damm, Alexander Pretschner, Jun Sun:
Integration of Formal Methods and Testing for Model-based Systems Engineering (NII Shonan Meeting 2014-16). NII Shonan Meet. Rep. 2014 (2014) - 2013
- [j24]Werner Damm, Hans-Jörg Peter, Jan-Hendrik Rakow, Bernd Westphal:
Can we build it: formal synthesis of control strategies for cooperative driver assistance systems. Math. Struct. Comput. Sci. 23(4): 676-725 (2013) - 2012
- [j23]Alberto L. Sangiovanni-Vincentelli
, Werner Damm, Roberto Passerone
:
Taming Dr. Frankenstein: Contract-Based Design for Cyber-Physical Systems. Eur. J. Control 18(3): 217-238 (2012) - [j22]Werner Damm, Henning Dierks, Stefan Disch, Willem Hagemann, Florian Pigorsch, Christoph Scholl, Uwe Waldmann, Boris Wirtz:
Exact and fully symbolic verification of linear hybrid automata with large discrete state spaces. Sci. Comput. Program. 77(10-11): 1122-1150 (2012) - [p3]Manfred Broy, Werner Damm, Stefan Henkler, Klaus Pohl, Andreas Vogelsang, Thorsten Weyer
:
Introduction to the SPES Modeling Framework. Model-Based Engineering of Embedded Systems 2012: 31-49 - 2011
- [j21]Werner Damm, Carsten Ihlemann, Viorica Sofronie-Stokkermans:
PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata. Math. Comput. Sci. 5(4): 469-497 (2011) - [c63]Werner Damm, Hardi Hungar, Bernhard Josko, Thomas Peikenkamp, Ingo Stierand:
Using contract-based component specifications for virtual integration testing and architecture design. DATE 2011: 1023-1028 - [c62]Werner Damm, Bernd Finkbeiner:
Does It Pay to Extend the Perimeter of a World Model? FM 2011: 12-26 - [c61]Matthias Büker, Werner Damm, Günter Ehmen, Ingo Stierand:
An Automated Semantic-Based Approach for Creating Tasks from Matlab Simulink Models. FMICS 2011: 149-164 - [c60]Jan-David Quesel, Martin Fränzle
, Werner Damm:
Crossing the Bridge between Similar Games. FORMATS 2011: 160-176 - [c59]Werner Damm, Carsten Ihlemann, Viorica Sofronie-Stokkermans:
Decidability and complexity for the verification of safety properties of reasonable linear hybrid automata. HSCC 2011: 73-82 - [c58]Matthias Büker, Werner Damm, Günter Ehmen, Alexander Metzner, Ingo Stierand, Eike Thaden
:
Automating the design flow for distributed embedded automotive applications: Keeping your time promises, and optimizing costs, too. SIES 2011: 156-165 - 2010
- [c57]Werner Damm, Henning Dierks, Jens Oehlerking, Amir Pnueli:
Towards Component Based Design of Hybrid Systems: Safety and Stability. Essays in Memory of Amir Pnueli 2010: 96-143
2000 – 2009
- 2009
- [j20]Roberto Passerone
, Imene Ben Hafaiedh, Susanne Graf, Albert Benveniste, Daniela Cancila, Arnaud Cuccuru, Sebastien Gerard
, François Terrier, Werner Damm, Alberto Ferrari, Leonardo Mangeruca, Bernhard Josko, Thomas Peikenkamp, Alberto L. Sangiovanni-Vincentelli
:
Metamodels in Europe: Languages, Tools, and Applications. IEEE Des. Test Comput. 26(3): 38-53 (2009) - 2008
- [c56]Harald Heinecke, Werner Damm, Bernhard Josko, Alexander Metzner, Hermann Kopetz, Alberto L. Sangiovanni-Vincentelli
, Marco Di Natale
:
Software Components for Reliable Automotive Systems. DATE 2008: 549-554 - [c55]Werner Damm:
Contract-Based Analysis of Automotive and Avionics Applications: The SPEEDS Approach. FMICS 2008: 3 - 2007
- [j19]Werner Damm, Guilherme Pinto, Stefan Ratschan:
Guaranteed Termination in the Verification of Ltl Properties of Non-linear Robust Discrete Time Hybrid Systems. Int. J. Found. Comput. Sci. 18(1): 63-86 (2007) - [j18]Bernd Becker
, Andreas Podelski, Werner Damm, Martin Fränzle
, Ernst-Rüdiger Olderog, Reinhard Wilhelm:
SFB/TR 14 AVACS - Automatic Verification and Analysis of Complex Systems (Der Sonderforschungsbereich/Transregio 14 AVACS - Automatische Verifikation und Analyse komplexer Systeme). it Inf. Technol. 49(2): 118-126 (2007) - [c54]Jörg Bauer, Werner Damm, Tobe Toben, Bernd Westphal:
Verification and Synthesis of OCL Constraints Via Topology Analysis. AGTIVE 2007: 361-376 - [c53]Werner Damm, Stefan Disch, Hardi Hungar, Swen Jacobs
, Jun Pang, Florian Pigorsch, Christoph Scholl, Uwe Waldmann, Boris Wirtz:
Exact State Set Representations in the Verification of Linear Hybrid Systems with Large Discrete State Space. ATVA 2007: 425-440 - [c52]Werner Damm, Alfred Mikschl, Jens Oehlerking, Ernst-Rüdiger Olderog, Jun Pang, André Platzer, Marc Segelken, Boris Wirtz:
Automating Verification of Cooperation, Control, and Design in Traffic Applications. Formal Methods and Hybrid Real-Time Systems 2007: 115-169 - [e3]Werner Damm, Holger Hermanns:
Computer Aided Verification, 19th International Conference, CAV 2007, Berlin, Germany, July 3-7, 2007, Proceedings. Lecture Notes in Computer Science 4590, Springer 2007, ISBN 978-3-540-73367-6 [contents] - 2006
- [c51]Werner Damm, Stefan Disch, Hardi Hungar, Jun Pang, Florian Pigorsch, Christoph Scholl, Uwe Waldmann, Boris Wirtz:
Automatic Verification of Hybrid Systems with Large Discrete State Space. ATVA 2006: 276-291 - [c50]Werner Damm, Tobe Toben, Bernd Westphal:
On the Expressive Power of Live Sequence Charts. Program Analysis and Compilation 2006: 225-246 - [c49]Werner Damm:
Embedded system development for automotive applications: trends and challenges. EMSOFT 2006: 1 - [c48]Werner Damm, Alexander Metzner, Friedrich Eisenbrand, Gennady Shmonin, Reinhard Wilhelm, Sebastian Winkel:
Mapping Task-Graphs on Distributed ECU Networks: Efficient Algorithms for Feasibility and Optimality. RTCSA 2006: 87-90 - 2005
- [j17]Werner Damm, Bernhard Josko, Amir Pnueli, Anjelika Votintseva:
A discrete-time UML semantics for concurrency and communication in safety-critical applications. Sci. Comput. Program. 55(1-3): 81-115 (2005) - [j16]Werner Damm, Bernd Westphal:
Live and let die: LSC based verification of UML models. Sci. Comput. Program. 55(1-3): 117-159 (2005) - [j15]Paul Caspi, Alberto L. Sangiovanni-Vincentelli, Luís Almeida
, Albert Benveniste, Bruno Bouyssounouse, Giorgio C. Buttazzo, Ivica Crnkovic
, Werner Damm, Jakob Engblom, Gerhard Fohler, Marisol García-Valls
, Hermann Kopetz, Yassine Lakhnech, François Laroussinie, Luciano Lavagno, Giuseppe Lipari, Florence Maraninchi, Philipp Peti, Juan Antonio de la Puente
, Norman Scaife, Joseph Sifakis, Robert de Simone, Martin Törngren
, Paulo Veríssimo, Andy J. Wellings, Reinhard Wilhelm, Tim A. C. Willemse
, Wang Yi:
Guidelines for a graduate curriculum on embedded software and systems. ACM Trans. Embed. Comput. Syst. 4(3): 587-611 (2005) - [c47]Werner Damm:
Controlling Speculative Design Processes Using Rich Component Models. ACSD 2005: 118-119 - [c46]Werner Damm, Guilherme Pinto, Stefan Ratschan:
Guaranteed Termination in the Verification of LTL Properties of Non-linear Robust Discrete Time Hybrid Systems. ATVA 2005: 99-113 - [c45]Udo Brockmeyer, Werner Damm, Hardi Hungar, Bernhard Josko:
Automatic Validation and Verification in a Model-Based Development Process. MBEES 2005: 113-124 - 2004
- [j14]Ralf Buschermöhle, Mark Brörkens, Ingo Brückner, Werner Damm, Wilhelm Hasselbring, Bernhard Josko, Christoph Schulte, Thomas Wolf:
Model Checking (Grundlagen und Praxiserfahrungen). Inform. Spektrum 27(2): 146-158 (2004) - [c44]Eckard Böde, Werner Damm, Jarl Høyem, Bernhard Josko, Jürgen Niehaus, Marc Segelken:
Adding Value to Automotive Models. ASWSD 2004: 86-102 - [c43]Werner Damm, Bernd Westphal:
Introduction to Subject Area 'Charts'. SoftSpez Final Report 2004: 322-324 - [c42]Matthias Brill, Werner Damm, Jochen Klose, Bernd Westphal, Hartmut Wittke:
Live Sequence Charts: An Introduction to Lines, Arrows, and Strange Boxes in the Context of Formal Verification. SoftSpez Final Report 2004: 374-399 - [c41]Matthias Brill, Ralf Buschermöhle, Werner Damm, Jochen Klose, Bernd Westphal, Hartmut Wittke:
Formal Verification of LSCs in the Development Process. SoftSpez Final Report 2004: 494-516 - [e2]Hartmut Ehrig, Werner Damm, Jörg Desel, Martin Große-Rhode, Wolfgang Reif, Eckehard Schnieder, Engelbert Westkämper:
Integration of Software Specification Techniques for Applications in Engineering, Priority Program SoftSpez of the German Research Foundation (DFG), Final Report. Lecture Notes in Computer Science 3147, Springer 2004, ISBN 3-540-23135-8 [contents] - 2003
- [j13]Martin Fränzle
, Jürgen Niehaus, Alexander Metzner, Werner Damm:
A Semantics for Distributed Execution of Statemate. Formal Aspects Comput. 15(4): 390-405 (2003) - [c40]Werner Damm, Hardi Hungar, Ernst-Rüdiger Olderog:
On the Verification of Cooperating Traffic Agents. FMCO 2003: 77-110 - [c39]Werner Damm, Christoph Schulte, Hartmut Wittke, Marc Segelken, Uwe Higgen, Michael Eckrich:
Formale Verifikation von ASCET Modellen im Rahmen der Entwicklung der Aktivlenkung. GI Jahrestagung (1) 2003: 340-344 - [c38]Werner Damm:
Recent Trends in the Development of Safety Critical Systems. FMICS 2003: 140 - 2002
- [c37]Werner Damm, Bernhard Josko, Amir Pnueli, Anjelika Votintseva:
Understanding UML: A Formal Semantics of Concurrency and Communication in Real-Time UML. FMCO 2002: 71-98 - [c36]Werner Damm, Bernd Westphal:
Live and Let Die: LSC-Based Verification of UML-Models. FMCO 2002: 99-135 - [c35]Werner Damm, Bengt Jonsson:
Eliminating Queues from RT UML Model Representations. FTRTFT 2002: 375-394 - [e1]Werner Damm, Ernst-Rüdiger Olderog:
Formal Techniques in Real-Time and Fault-Tolerant Systems, 7th International Symposium, FTRTFT 2002, Co-sponsored by IFIP WG 2.2, Oldenburg, Germany, September 9-12, 2002, Proceedings. Lecture Notes in Computer Science 2469, Springer 2002, ISBN 3-540-44165-4 [contents] - 2001
- [j12]Werner Damm, David Harel:
LSCs: Breathing Life into Message Sequence Charts. Formal Methods Syst. Des. 19(1): 45-80 (2001) - [j11]Werner Damm, Jochen Klose:
Verification of a Radio-Based Signaling System Using the STATEMATE Verification Environment. Formal Methods Syst. Des. 19(2): 121-141 (2001) - [j10]Tom Bienmüller, Werner Damm, Jochen Klose, Hartmut Wittke:
Formale Analyse und Verifikation von Statemate-Entwürfen (Formal Analysis and Verification of Statemate Designs). Informationstechnik Tech. Inform. 43(1): 29-34 (2001) - [c34]Werner Damm:
Understanding UML - Pains and Rewards. UML 2001: 240 - 2000
- [j9]Hans-Jürgen Appelrath, Werner Damm, K.-H. Menke, Wolfgang Nebel, Wilfried Thoben:
OFFIS - Acht Jahre anwendungsorientierte Informatik-Forschung und -Entwicklung. Inform. Forsch. Entwickl. 15(1): 51-61 (2000) - [j8]Jürgen Niehaus, Werner Damm, Alexander Metzner, Alfred Mikschl:
Die EVENTS-Architektur (The EVENTS Architecture). Informationstechnik Tech. Inform. 42(2): 40-44 (2000) - [c33]Tom Bienmüller, Werner Damm, Hartmut Wittke:
The STATEMATE Verification Environment - Making It Real. CAV 2000: 561-567 - [c32]Werner Damm:
Challenges in the Verification of Electronic Control Units. FTRTFT 2000: 18 - [c31]Werner Damm:
Offering Formal Verification Capabilities for Industry Standard Case Tools: Challenges and Results. ICFEM 2000: 153
1990 – 1999
- 1999
- [c30]Tom Bienmüller, Jürgen Bohn, Henning Brinkmann, Udo Brockmeyer, Werner Damm, Hardi Hungar, Peter Jansen:
Verification of Automotive Control Units. Correct System Design 1999: 319-341 - [c29]Werner Damm, David Harel:
LSCs: Breathing Life into Message Sequence Charts. FMOODS 1999 - 1998
- [c28]Werner Damm, Amir Pnueli, Sitvanit Ruah:
Herbrand Automata for Hardware Verification. CONCUR 1998: 67-83 - [c27]Jürgen Bohn, Werner Damm, Orna Grumberg, Hardi Hungar, Karen Laster:
First-Order-CTL Model Checking. FSTTCS 1998: 283-294 - [c26]Werner Damm:
Verifying electronic control unit: today and tomorrow. PROCOMET 1998: 7-8 - 1997
- [c25]Werner Damm, Amir Pnueli:
Verifying out-of-order executions. CHARME 1997: 23-47 - [c24]Werner Damm, Bernhard Josko, Hardi Hungar, Amir Pnueli:
A Compositional Real-Time Semantics of STATEMATE Designs. COMPOS 1997: 186-238 - 1996
- [c23]Jürgen Risau, Alfred Mikschl, Werner Damm:
A RISC Approach to Weak Cache Coherence. Euro-Par, Vol. II 1996: 453-456 - [c22]Alfred Mikschl, Werner Damm:
MSparc: A Multithreaded Sparc. Euro-Par, Vol. II 1996: 461-469 - 1995
- [c21]Feixiong Liu, Thomas Peikenkamp, Werner Damm:
An Extended Gradient Model for NUMA Multiprocessor Systems. ASIAN 1995: 210-224 - [c20]Hardi Hungar, Orna Grumberg, Werner Damm:
What if model checking must be truly symbolic. CHARME 1995: 1-20 - [p2]Werner Damm, Hardi Hungar, Peter Kelb, Rainer Schlör:
Statecharts. Formal Development of Reactive Systems 1995: 131-149 - 1994
- [c19]Werner Damm, Johannes Helbig:
Linking Visual Formalisms: A Compositional Proof System for Statecharts Based on Symbolic Timing Diagrams. PROCOMET 1994: 341-359 - 1993
- [j7]Johannes Helbig, Rainer Schlör, Werner Damm, Gert Döhmen, Peter Kelb:
VHDL/S - integrating statecharts, timing diagrams, and VHDL. Microprocess. Microprogramming 38(1-5): 571-580 (1993) - [c18]Costas Courcoubetis, Werner Damm, Bernhard Josko:
Verification of timing Properties of VHDL. CAV 1993: 225-236 - [c17]Werner Damm, Bernhard Josko, Rainer Schlör:
A net-based semantics for VHDL. EURO-DAC 1993: 514-519 - [p1]Werner Damm, Bernhard Josko, Rainer Schlör:
Specification and verification of VHDL-based system-level hardware designs. Specification and validation methods 1993: 331-409
1980 – 1989
- 1989
- [j6]Werner Damm, Gert Döhmen:
Specifying distributed computer architectures in AADL. Parallel Comput. 9(2): 193-211 (1989) - [c16]Rita Loogen, Herbert Kuchen, Klaus Indermark, Werner Damm:
Distributed Implementation of Programmed Graph Reduction. PARLE (1) 1989: 136-157 - [c15]Werner Damm, Gert Döhmen, Volker Gerstner, Bernhard Josko:
Modular Verification of Petri Nets: The Temporal Logic Approach. REX Workshop 1989: 180-207 - 1988
- [j5]Werner Damm:
A Microprogramming Logic. IEEE Trans. Software Eng. 14(5): 559-574 (1988) - 1987
- [b1]Werner Damm:
Entwurf und Verifikation mikroprogrammierter Rechnerarchitekturen. Informatik-Fachberichte 146, Springer 1987, ISBN 3-540-18320-5 - [c14]Werner Damm, Gert Döhmen:
An Axiomatic Approach to the Specification of Distributed Computer Architectures. PARLE (1) 1987: 103-120 - 1986
- [j4]Werner Damm, Andreas Goerdt:
An Automata-Theoretical Characterization of the OI-Hierarchy. Inf. Control. 71(1/2): 1-32 (1986) - [j3]Werner Damm, Gert Döhmen, Klaus Merkel, Mathilde Sichelschmidt:
The AADL/S* Approach to Firmware Design Verification. IEEE Softw. 3(4): 27-37 (1986) - 1985
- [c13]Werner Damm:
Design and specification of microprogrammed computer architectures. MICRO 1985: 3-10 - [c12]Werner Damm, Gert Döhmen:
Verification of microprogrammed computer architectures in the S*-system: a case study. MICRO 1985: 61-73 - 1984
- [c11]Werner Damm:
An axiomatization of low-level parallelism in microarchitectures. MICRO 1984: 314-323 - 1983
- [j2]Werner Damm, Bernhard Josko:
A Sound and Relatively * Complete Hoare-Logic for a Language With Higher Type Procedures. Acta Informatica 20: 59-101 (1983) - [c10]Werner Damm, Bernhard Josko:
A Sound and Relatively* Compete Axiomatization of Clarke's Language L4. Logic of Programs 1983: 161-175 - 1982
- [j1]Werner Damm:
The IO- and OI-Hierarchies. Theor. Comput. Sci. 20: 95-207 (1982) - [c9]Werner Damm, Andreas Goerdt:
An Automata-Theoretic Characterization of the OI-Hierarchy. ICALP 1982: 141-153 - 1981
- [c8]J. Bilstein, Werner Damm:
Top-Down Tree-Transducers for Infinite Trees I. CAAP 1981: 117-134 - [c7]Werner Damm, Irène Guessarian:
Combining T and level-N. MFCS 1981: 262-270 - 1980
- [c6]Werner Damm, Elfriede Fehr:
A schematalogical approach to the alalysis of the procedure concept in algol-languages. CLAAP 1980: 130-134
1970 – 1979
- 1979
- [c5]Werner Damm:
An Algebraic Extension of the Chomsky-Hierarchy. MFCS 1979: 266-276 - 1978
- [c4]Werner Damm, Elfriede Fehr:
On the Power of Self-Application and Higher Type-Recursion. ICALP 1978: 177-191 - 1977
- [c3]Werner Damm:
Languages Defined by Higher Type Program Schemes. ICALP 1977: 164-179 - [c2]Werner Damm, Elfriede Fehr, Klaus Indermark:
Higher Type Recursion and Self-Application as Control Structures. Formal Description of Programming Concepts 1977: 461-490 - [c1]Werner Damm:
Higher type program schemes and their tree languages. Theoretical Computer Science 1977: 51-72