18 research outputs found
Comparing Labelled Markov Decision Processes
A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one
Dynamic Probabilistic Input Output Automata
We present probabilistic dynamic I/O automata, a framework to model dynamic probabilistic systems. Our work extends dynamic I/O Automata formalism of Attie & Lynch [Paul C. Attie and Nancy A. Lynch, 2016] to the probabilistic setting. The original dynamic I/O Automata formalism included operators for parallel composition, action hiding, action renaming, automaton creation, and behavioral sub-typing by means of trace inclusion. They can model mobility by using signature modification. They are also hierarchical: a dynamically changing system of interacting automata is itself modeled as a single automaton. Our work extends all these features to the probabilistic setting. Furthermore, we prove necessary and sufficient conditions to obtain the monotonicity of automata creation/destruction with implementation preorder. Our construction uses a novel proof technique based on homomorphism that can be of independent interest. Our work lays down the foundations for extending composable secure-emulation of Canetti et al. [Ran Canetti et al., 2007] to dynamic settings, an important tool towards the formal verification of protocols combining probabilistic distributed systems and cryptography in dynamic settings (e.g. blockchains, secure distributed computation, cybersecure distributed protocols, etc)
Strategies for MDP Bisimilarity Equivalence and Inequivalence
A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. Motivated by applications to the verification of probabilistic noninterference in security, we study problems whether there exist strategies such that the labelled MDPs become bisimilarity equivalent/inequivalent. We show that the equivalence problem is decidable; in fact, it is EXPTIME-complete and becomes NP-complete if one of the MDPs is a Markov chain. Concerning the inequivalence problem, we show that (1) it is decidable in polynomial time; (2) if there are strategies for inequivalence then there are memoryless strategies for inequivalence; (3) such memoryless strategies can be computed in polynomial time
Solving Odd-Fair Parity Games
This paper discusses the problem of efficiently solving parity games where
player Odd has to obey an additional 'strong transition fairness constraint' on
its vertices -- given that a player Odd vertex is visited infinitely often,
a particular subset of the outgoing edges (called live edges) of has to be
taken infinitely often. Such games, which we call 'Odd-fair parity games',
naturally arise from abstractions of cyber-physical systems for planning and
control.
In this paper, we present a new Zielonka-type algorithm for solving Odd-fair
parity games. This algorithm not only shares 'the same worst-case time
complexity' as Zielonka's algorithm for (normal) parity games but also
preserves the algorithmic advantage Zielonka's algorithm possesses over other
parity solvers with exponential time complexity.
We additionally introduce a formalization of Odd player winning strategies in
such games, which were unexplored previous to this work. This formalization
serves dual purposes: firstly, it enables us to prove our Zielonka-type
algorithm; secondly, it stands as a noteworthy contribution in its own right,
augmenting our understanding of additional fairness assumptions in two-player
games.Comment: To be published in FSTTCS 202