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
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Model Checking of Unrestricted Hierarchical State Machines
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
Analysis of Recursive State Machines
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Estimation of probabilistic context-free grammars
Computational Linguistics
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
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Applying Probability Measures to Abstract Languages
IEEE Transactions on Computers
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Probabilistic Context-Free Grammars Estimated from Infinite Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
CSL model checking algorithms for QBDs
Theoretical Computer Science
Computation of distances for regular and context-free probabilistic languages
Theoretical Computer Science
Newton's Method for ω-Continuous Semirings
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Automata, Probability, and Recursion
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Derivation Tree Analysis for Accelerated Fixed-Point Computation
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
Discounted Properties of Probabilistic Pushdown Automata
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Axiomatizing rational power series over natural numbers
Information and Computation
Branching-Time Model-Checking of Probabilistic Pushdown Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
Parsing algorithms based on tree automata
IWPT '09 Proceedings of the 11th International Conference on Parsing Technologies
Methods for Quantitative Analysis of Probabilistic Pushdown Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
On fixed point equations over commutative semirings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
An extension of Newton's method to ω-continuous semirings
DLT'07 Proceedings of the 11th international conference on Developments in language theory
CSL model checking algorithms for infinite-state structured Markov chains
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
SDSIrep: a reputation system based on SDSI
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Time-bounded reachability in tree-structured QBDs by abstraction
Performance Evaluation
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
TOOLS'11 Proceedings of the 49th international conference on Objects, models, components, patterns
Efficient analysis of probabilistic programs with an unbounded counter
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Carrying probabilities to the infinite world
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Two variable vs. linear temporal logic in model checking and games
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
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
Computing the expected accumulated reward and gain for a subclass of infinite markov chains
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Computation of infix probabilities for probabilistic context-free grammars
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Model checking probabilistic systems against pushdown specifications
Information Processing Letters
Analysis of recursive probabilistic models
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Consistency of stochastic context-free grammars
Mathematical and Computer Modelling: An International Journal
Determinacy and optimal strategies in infinite-state stochastic reachability games
Theoretical Computer Science
Tulip: model checking probabilistic systems using expectation maximisation algorithm
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Branching-time model-checking of probabilistic pushdown automata
Journal of Computer and System Sciences
Analyzing probabilistic pushdown automata
Formal Methods in System Design
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We introduce and study Recursive Markov Chains (RMCs), which extend ordinary finite state Markov chains with the ability to invoke other Markov chains in a potentially recursive manner. They offer a natural abstract model for probabilistic programs with procedures, and are a probabilistic version of Recursive State Machines. RMCs generalize Stochastic Context-Free Grammars (SCFG) and multi-type Branching Processes, and are intimately related to Probabilistic Pushdown Systems. We focus here on termination and reachability analysis for RMCs. We present both positive and negative results for the general class of RMCs, as well as for important subclasses including SCFGs.