Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A problem that is easier to solve on the unit-cost algebraic RAM
Journal of Complexity
The complexity of stochastic games
Information and Computation
The complexity of probabilistic verification
Journal of the ACM (JACM)
Competitive Markov decision processes
Competitive Markov decision processes
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Random walks with “back buttons” (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Model checking of hierarchical state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reachability Analysis of Pushdown Automata: Application to Model-Checking
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
Efficient Algorithms for Model Checking Pushdown Systems
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Model checking for probability and time: from theory to practice
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Quantitative solution of omega-regular games
Journal of Computer and System Sciences - STOC 2001
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Relating probabilistic grammars and automata
ACL '99 Proceedings of the 37th annual meeting of the Association for Computational Linguistics on Computational Linguistics
Analysis of recursive state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Quantitative Analysis of Probabilistic Pushdown Automata: Expectations and Variances
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Checking LTL Properties of Recursive Markov Chains
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
On the convergence of Newton's method for monotone systems of polynomial equations
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Approximative Methods for Monotone Systems of Min-Max-Polynomial Equations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Recursive Stochastic Games with Positive Rewards
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
PReMo: an analyzer for probabilistic recursive models
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Recursive concurrent stochastic games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Algorithmic verification of recursive probabilistic state machines
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Reachability in recursive markov decision processes
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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We discuss work on the modeling and analysis of systems with probabilistic and recursive features. Recursive Markov chains extend ordinary finite state Markov chains with the ability to invoke other Markov chains in a potentially recursive manner. The equivalent model of Probabilistic Pushdown Automata extends ordinary pushdown automata with probabilistic actions. Both of these are natural abstract models for probabilistic programs with procedures, and related systems. They generalize other classical well-studied stochastic models, e.g. Stochastic Context-free Grammars and (Multi-type) Branching Processes, that arise in a variety of areas. More generally, Recursive Markov Decision Processes and Recursive Stochastic Games can be used to model recursive systems that have both probabilistic and nonprobabilistic, controllable actions. In recent years there has been substantial work on the algorithmic analysis of these models, regarding basic questions of termination, reachability, and analysis of the properties of their executions. In this talk we will present some of the basic theory, algorithmic methods, results, and challenges.