Linear vs. branching time: A semantical perspective

The discussion of the relative merits of linear versus branching-time goes back to early 1980s. The dominating belief has been that the linear-time framework is not expressive enough semantically, marking linear-time logics as weak. Here we examine this issue from the perspective of process equivalence, one of the most fundamental notions in concurrency theory. We postulate three principles that we view as fundamental to any discussion of process equivalence. First, we take contextual equivalence as the primary notion of equivalence. Second, we require the description of a process to fully specify all relevant behavioral aspects of the process. Finally, we require observable process behavior to be reflected in input/output behavior. Under these postulates the distinctions between the linear and branching semantics tend to evaporate. Applying them to the framework of transducers, we show that our postulates result in a unique notion of process equivalence, which is trace based, rather than tree based

Synthesis from Probabilistic Components

Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms, it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course, rarely happens in real life, where almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. Recently, Lustig and Vardi introduced dataflow and control-flow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while control-flow synthesis is decidable. In this work, we consider the problem of control-flow synthesis from libraries of probabilistic components. We show that this more general problem is also decidable

IST Austria Technical Report

We consider two-player partial-observation stochastic games where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are omega-regular conditions specified as parity objectives. The qualitative analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, they were shown to be decidable in 2EXPTIME under finite-memory strategies. We improve the complexity and show that the qualitative analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis

Bisimilarity is not Finitely Based over BPA with Interrupt

This paper shows that bisimulation equivalence does not afford a finite equational axiomatization over the language obtained by enriching Bergstra and Klop's Basic Process Algebra with the interrupt operator. Moreover, it is shown that the collection of closed equations over this language is also not finitely based

Synthesis from Probabilistic Components

Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms, it is always assumed that the system is ``constructed from scratch'' rather than composed from reusable components. This, of course, rarely happens in real life, where almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. In contrast to classical synthesis, synthesis from components aims to build the desired system using components from a given library. In this dissertation, we consider the problem of control-flow synthesis from libraries of probabilistic components. We develop an automata-theoretic approach to solve the problem, investigate the expressive power of probabilistic control-flow, and examine the close relationship between synthesis from components and games with partial information

Trace Semantics Is Fully Abstract ∗

The discussion in the computer-science literature of the relative merits of linear- versus branching-time frameworks goes back to the early 1980s. One of the beliefs dominating this discussion has been that the linear-time framework is not expressive enough semantically, making linear-time logics lacking in expressiveness. In this work we examine the branching-linear issue from the perspective of process equivalence, which is one of the most fundamental concepts in concurrency theory, as defining a notion of equivalence essentially amounts to defining semantics for processes. We accept three principles that have been recently proposed for concurrent-process equivalence. The first principle takes contextual equivalence as the primary notion of equivalence. The second principle requires the description of a process to specify all relevant behavioral aspects of the process. The third principle requires observable process behavior to be reflected in its input/output behavior. It has been recently shown that under these principles trace semantics for nondeterministic transducers is fully abstract. Here we consider two extensions of the earlier model: probabilistic transducers and asynchronous transducers. We show that in both cases trace semantics is fully abstract.

Solving Partial-Information Stochastic Parity Games

We study one-sided partial-information 2-player concurrent stochastic games with parity objectives. In such a game, one of the players has only partial visibility of the state of the game, while the other player has complete knowledge. In general, such games are known to be undecidable, even for the case of a single player (POMDP). These undecidability results depend crucially on player strategies that exploit an infinite amount of memory. However, in many applications of games, one is usually more interested in finding a finite-memory strategy. We consider the problem of whether the player with partial information has a finite-memory winning strategy when the player with complete information is allowed to use an arbitrary amount of memory. We show that this problem is decidable. 1

Bisimilarity is not finitely based over BPA with interrupt

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