A Study in the Computational Complexity of Temporal Reasoning

Reasoning about temporal and spatial information is a common task in computer science, especially in the field of artificial intelligence. The topic of this thesis is the study of such reasoning fr ...

[1]  Frank D. Anger,et al.  Lattice structure of temporal interval relations , 2004, Applied Intelligence.

[2]  Christer Bäckström,et al.  A Unifying Approach to Temporal Constraint Reasoning , 1998, Artif. Intell..

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Peter Jonsson,et al.  A Complete Classification of Tractability in RCC-5 , 1997, J. Artif. Intell. Res..

[5]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[6]  Henry A. Kautz,et al.  Constraint propagation algorithms for temporal reasoning: a revised report , 1989 .

[7]  Abdul Sattar,et al.  A New Framework for Reasoning about Points, Intervals and Durations , 1999, IJCAI.

[8]  Drew McDermott,et al.  A Temporal Logic for Reasoning About Processes and Plans , 1982, Cogn. Sci..

[9]  Rina Dechter,et al.  Temporal Constraint Networks , 1989, Artif. Intell..

[10]  Pravin M. Vaidya,et al.  An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations , 1987, Math. Program..

[11]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[12]  Ron Shamir,et al.  Complexity and algorithms for reasoning about time: a graph-theoretic approach , 1993, JACM.

[13]  Peter Jeavons,et al.  A Survey of Tractable Constraint Satisfaction Problems , 1997 .

[14]  Peter van Beek,et al.  On the minimality and global consistency of row-convex constraint networks , 1995, JACM.

[15]  Peter Jeavons,et al.  Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra , 2003, JACM.

[16]  Jochen Renz,et al.  A Spatial Odyssey of the Interval Algebra: 1. Directed Intervals , 2001, IJCAI.

[17]  Manolis Koubarakis,et al.  Tractable Disjunctions of Linear Constraints , 1996, CP.

[18]  Ivo Düntsch,et al.  Relations Algebras in Qualitative Spatial Reasoning , 1999, Fundam. Informaticae.

[19]  Pascal Van Hentenryck,et al.  Constraint Satisfaction over Connected Row Convex Constraints , 1997, Artif. Intell..

[20]  Christer Bäckström,et al.  Computational Complexity of Relating Time Points with Intervals , 1999, Artif. Intell..

[21]  Alan K. Mackworth Consistency in Networks of Relations , 1977, Artif. Intell..

[22]  Eugene C. Freuder A sufficient condition for backtrack-bounded search , 1985, JACM.

[23]  Jean-Frann Cois Condotta,et al.  The Augmented Interval and Rectangle Networks , 2022 .

[24]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[25]  Kenneth L. McMillan,et al.  Symbolic model checking: an approach to the state explosion problem , 1992 .

[26]  Peter Jonsson,et al.  Towards a Complete Classification of Tractability in Point Algebras for Nonlinear Time , 1999, CP.

[27]  Peter Jonsson,et al.  Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time , 1997, J. Artif. Intell. Res..

[28]  Glynn Winskel,et al.  An introduction to event structures , 1988, REX Workshop.

[29]  Frank D. Anger,et al.  On Lamport's interprocessor communication model , 1989, TOPL.

[30]  Toby Walsh,et al.  Search on High Degree Graphs , 2001, IJCAI.

[31]  Manolis Koubarakis,et al.  Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning , 2001, Theor. Comput. Sci..

[32]  Tad Hogg,et al.  Refining the Phase Transition in Combinatorial Search , 1996, Artif. Intell..

[33]  Glynn Winskel,et al.  An Introduction to Event Structures , 1989 .

[34]  Marcus Bjäreland,et al.  Reasoning about Action in Polynomial Time , 1997, IJCAI.

[35]  Jai Srinivasan,et al.  Branching time temporal logic , 1988, REX Workshop.

[36]  Alfonso Gerevini,et al.  On Finding a Solution in Temporal Constraint Satisfaction Problems , 1997, IJCAI.

[37]  Peter Jeavons,et al.  New Tractable Classes from Old , 2000, CP.

[38]  Frank D. Anger,et al.  Using Constraint Propagation to Reason about Unsynchronized Clocks , 1998, Constraints.

[39]  Peter Jeavons,et al.  Building tractable disjunctive constraints , 2000, J. ACM.

[40]  Marcus Bjäreland,et al.  Expressive Reasoning about Action in Nondeterministic Polynomial Time , 1999, IJCAI.

[41]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[42]  James F. Allen Maintaining knowledge about temporal intervals , 1983, CACM.

[43]  Christian Bessiere,et al.  Global Consistency in Interval Algebra Networks: Tractable Subclasses , 1996, ECAI.

[44]  Bernhard Nebel,et al.  On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus , 1999, Artif. Intell..

[45]  Leslie Lamport,et al.  The mutual exclusion problem: part I—a theory of interprocess communication , 1986, JACM.

[46]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[47]  Brandon Bennett,et al.  Spatial Reasoning with Propositional Logics , 1994, KR.

[48]  Manolis Koubarakis,et al.  Backtracking algorithms for disjunctions of temporal constraints , 1998, Artif. Intell..

[49]  Mark S. Boddy,et al.  Reasoning About Partially Ordered Events , 1988, Artificial Intelligence.

[50]  Bernhard Nebel Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class , 1997 .

[51]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[52]  Peter Jonsson,et al.  Refinements and Independence: A Simple Method for Identifying Tractable Disjunctive Constraints , 2000, CP.

[53]  Leslie Lamport,et al.  Time, clocks, and the ordering of events in a distributed system , 1978, CACM.

[54]  Mathias Broxvall The Point Algebra for Branching Time Revisited , 2001, KI/ÖGAI.

[55]  Peter Jonsson,et al.  Disjunctions, independence, refinements , 2002, Artif. Intell..

[56]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas , 1979, Inf. Process. Lett..

[57]  Allen Van Gelder,et al.  Computer Algorithms: Introduction to Design and Analysis , 1978 .

[58]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[59]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[60]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[61]  Luis Fariñas del Cerro,et al.  A New Tractable Subclass of the Rectangle Algebra , 1999, IJCAI.

[62]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[63]  Bernhard Nebel,et al.  Efficient Methods for Qualitative Spatial Reasoning , 2001, J. Artif. Intell. Res..

[64]  Marc Gyssens,et al.  Decomposing Constraint Satisfaction Problems Using Database Techniques , 1994, Artif. Intell..

[65]  Georg Gottlob,et al.  A Comparison of Structural CSP Decomposition Methods , 1999, IJCAI.

[66]  M. Yannakakis The Complexity of the Partial Order Dimension Problem , 1982 .

[67]  Jochen Renz,et al.  Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis , 1999, IJCAI.

[68]  Bernhard Nebel,et al.  Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class , 1997, Constraints.

[69]  Robin Hirsch,et al.  Expressive Power and Complexity in Algebraic Logic , 1997, J. Log. Comput..