Matrix analysis
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Modularity of cycles and paths in graphs
Journal of the ACM (JACM)
Journal of Symbolic Computation
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)
Complexity and real computation
Complexity and real computation
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
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Model checking of hierarchical state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
On the Power of Random Access Machines
Proceedings of the 6th 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
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A characterization of the class of functions computable in polynomial time on Random Access Machines
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
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
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
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
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
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
Applying Probability Measures to Abstract Languages
IEEE Transactions on Computers
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
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
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
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
Stochastic models for tabbed browsing
Proceedings of the 19th international conference on World wide web
Querying parse trees of stochastic context-free grammars
Proceedings of the 13th International Conference on Database Theory
On least fixed points of systems of positive polynomials
ACM Communications in Computer Algebra
Journal of the ACM (JACM)
Space-efficient scheduling of stochastically generated tasks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
On models and query languages for probabilistic processes
ACM SIGMOD Record
Probabilistic XML via Markov Chains
Proceedings of the VLDB Endowment
Querying probabilistic business processes for sub-flows
Proceedings of the 14th International Conference on Database Theory
Computing the Least Fixed Point of Positive Polynomial Systems
SIAM Journal on Computing
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
On probabilistic parallel programs with process creation and synchronisation
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
A quest for beauty and wealth (or, business processes for database researchers)
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Runtime analysis of probabilistic programs with unbounded recursion
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Space-efficient scheduling of stochastically generated tasks
Information and Computation
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
Computation of infix probabilities for probabilistic context-free grammars
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Model Checking of Recursive Probabilistic Systems
ACM Transactions on Computational Logic (TOCL)
Prefix probabilities for linear context-free rewriting systems
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
Polynomial time algorithms for multi-type branching processesand stochastic context-free grammars
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the complexity of the equivalence problem for probabilistic automata
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Finding optimal probabilistic generators for XML collections
Proceedings of the 15th International Conference on Database Theory
Survey: Equilibria, fixed points, and complexity classes
Computer Science Review
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Model checking stochastic branching processes
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Model checking with probabilistic tabled logic programming
Theory and Practice of Logic Programming
On the complexity of model checking interval-valued discrete time Markov chains
Information Processing Letters
Search and result presentation in scientific workflow repositories
Proceedings of the 25th International Conference on Scientific and Statistical Database Management
Top-k queries over web applications
The VLDB Journal — The International Journal on Very Large Data Bases
Stochastic context-free grammars, regular languages, and newton's method
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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 define Recursive Markov Chains (RMCs), a class of finitely presented denumerable Markov chains, and we study algorithms for their analysis. Informally, an RMC consists of a collection of finite-state Markov chains with the ability to invoke each other in a potentially recursive manner. RMCs offer a natural abstract model for probabilistic programs with procedures. They generalize, in a precise sense, a number of well-studied stochastic models, including Stochastic Context-Free Grammars (SCFG) and Multi-Type Branching Processes (MT-BP). We focus on algorithms for reachability and termination analysis for RMCs: what is the probability that an RMC started from a given state reaches another target state, or that it terminates? These probabilities are in general irrational, and they arise as (least) fixed point solutions to certain (monotone) systems of nonlinear equations associated with RMCs. We address both the qualitative problem of determining whether the probabilities are 0, 1 or in-between, and the quantitative problems of comparing the probabilities with a given bound, or approximating them to desired precision. We show that all these problems can be solved in PSPACE using a decision procedure for the Existential Theory of Reals. We provide a more practical algorithm, based on a decomposed version of multi-variate Newton's method, and prove that it always converges monotonically to the desired probabilities. We show this method applies more generally to any monotone polynomial system. We obtain polynomial-time algorithms for various special subclasses of RMCs. Among these: for SCFGs and MT-BPs (equivalently, for 1-exit RMCs) the qualitative problem can be solved in P-time; for linearly recursive RMCs the probabilities are rational and can be computed exactly in P-time. We show that our PSPACE upper bounds cannot be substantially improved without a breakthrough on long standing open problems: the square-root sum problem and an arithmetic circuit decision problem that captures P-time on the unit-cost rational arithmetic RAM model. We show that these problems reduce to the qualitative problem and to the approximation problem (to within any nontrivial error) for termination probabilities of general RMCs, and to the quantitative decision problem for termination (extinction) of SCFGs (MT-BPs).