Randomized algorithms
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
Symbolic Model Checking for Probabilistic Processes
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Synthesis of Linear Ranking Functions
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Statistical probabilistic model checking with a focus on time-bounded properties
Information and Computation
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
PRISM: probabilistic model checking for performance and reliability analysis
ACM SIGMETRICS Performance Evaluation Review
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Termination of polynomial programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Proving positive almost-sure termination
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A generalization of p-boxes to affine arithmetic
Computing - Special Issue on GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN2010)
Probabilistic abstract interpretation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Proving termination of probabilistic programs using patterns
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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We present techniques for the analysis of infinite state probabilistic programs to synthesize probabilistic invariants and prove almost-sure termination. Our analysis is based on the notion of (super) martingales from probability theory. First, we define the concept of (super) martingales for loops in probabilistic programs. Next, we present the use of concentration of measure inequalities to bound the values of martingales with high probability. This directly allows us to infer probabilistic bounds on assertions involving the program variables. Next, we present the notion of a super martingale ranking function (SMRF) to prove almost sure termination of probabilistic programs. Finally, we extend constraint-based techniques to synthesize martingales and super-martingale ranking functions for probabilistic programs. We present some applications of our approach to reason about invariance and termination of small but complex probabilistic programs.