The complexity of probabilistic verification

  title={The complexity of probabilistic verification},
  author={Costas A. Courcoubetis and Mihalis Yannakakis},
  journal={J. ACM},
We determine the complexity of testing whether a finite state, sequential or concurrent probabilistic program satisfies its specification expressed in linear-time temporal logic. For sequential programs, we present an algorithm that runs in time linear in the program and exponential in the specification, and also show that the problem is in PSPACE, matching the known lower bound. For concurrent programs, we show that the problem can be solved in time polynomial in the program and doubly… 

Figures from this paper

Computing Probability Bounds for Linear Time Formulas over Concurrent Probabilistic Systems

Quantitative Analysis of Randomized Distributed Systems and Probabilistic Automata

The automata-based model checking approach for randomized distributed systems relies on an operational interleaving semantics of the system by means of a Markov decision process (MDP) and a

Model Checking Probabilistic Systems

This work presents the implementation of an efficient model checking tool for formulas of a formal probabilistic logic (EPPL) over non-reliable digital circuits, and considers factorizations of stochastic processes associated with the probability spaces generated by the systems.

Probabilistic verification and approximation

Model checking probabilistic pushdown automata

  • A. KuceraJ. EsparzaR. Mayr
  • Computer Science
    Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
  • 2004
This work considers the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various Probabilistic logics and proves that both qualitative and quantitative model checking for pPDA is decidable.

Model Checking of Recursive Probabilistic Systems

This article studies the problem of model checking an RMC against an ω-regular specification, given in terms of a Büchi automaton or a Linear Temporal Logic (LTL) formula, and establishes a number of strong upper bounds, as well as lower bounds, both for qualitative and quantitative problems.

Verification of Probabilistic Recursive Sequential Programs

This work studies algorithmic verification of infinite-state probabilistic systems generated by probabilistic pushdown automata (pPDA). Probabilistic pushdown automata are obtained as a probabilistic

Automata-Theoretic Verification

The automata-theoretic approach to the satisfiability and model-checking problems for temporal logics reduces these problems to standard decision problems about automata, like nonemptiness, language containment, or membership (whether a given object is accepted by a given automaton).

Two Variable vs. Linear Temporal Logic in Model Checking and Games

This paper gives two logic-to-automata translations which can be used to give upper bounds for FO2 and UTL, and applies these to get new bounds for both nondeterministic systems and probabilistic systems, including Markov chains and Markov decision processes.

Bounded Probabilistic Model Checking with the Muralpha Verifier

An explicit verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains and checks if Φ is satisfied in \({\cal M}\).



Automatic verification of probabilistic concurrent finite state programs

  • Moshe Y. Vardi
  • Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
An automata-theoretic approach is described, whereby probabilistic quantification over sets of computations is reduced to standard quantificationover individual computations, and a new determinization construction for ω-automata is used to improve the time complexity of the algorithm by two exponentials.

Checking that finite state concurrent programs satisfy their linear specification

An algorithm for checking satisfiability of a linear time temporal logic formula over a finite state concurrent program and a formal proof in case the formula is valid over the program is presented.

Automatic verification of finite state concurrent system using temporal logic specifications: a practical approach

It is argued that this technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finite state concurrent systems.

Reasoning with Time and Chance

The complexity of propositional linear temporal logics

We consider the complexity of satisfiability and determination of truth in a particular finite structure for different propositional linear temporal logics. We show that both the above problems are

Termination of Probabilistic Concurrent Program

In this model synchronization protocols that use randomization are in certain cases no more powerful than deterministic protocols and no fully symmetric randomized protocol can ensure mutual exclusion and freedom from lockout.

Reasoning about infinite computation paths

This work investigates extensions of temporal logic by finite automata on infinite words by investigating the addition of alternation and shows that it does not increase the complexity of the decision problem.


This work defines alternating Turing Machines which are like nondeterministic Turing Machines, except that existential and universal quantifiers alternate, and shows that while n-state alternating finite automata accept only regular sets that can be accepted by 22n-O(logn) state deterministic automata, alternating pushdown automata acceptance all languages accepted by Turing machines in deterministic exponential time.