A distributed protocol is typically modeled as a set of communicating processes, where each process is described as an extended state machine along with fairness assumptions, and its correctness is specified using safety and liveness requirements. De
signing correct distributed protocols is a challenging task. Aimed at simplifying this task, we allow the designer to leave some of the guards and updates to state variables in the description of extended state machines as unknown functions. The protocol completion problem then is to find interpretations for these unknown functions while guaranteeing correctness. In many distributed protocols, process behaviors are naturally symmetric, and thus, synthesized expressions are further required to obey symmetry constraints. Our counterexample-guided synthesis algorithm consists of repeatedly invoking two phases. In the first phase, candidates for unknown expressions are generated using the SMT solver Z3. This phase requires carefully orchestrating constraints to enforce the desired symmetry in read/write accesses. In the second phase, the resulting completed protocol is checked for correctness using a custom-built model checker that handles fairness assumptions, safety and liveness requirements, and exploits symmetry. When model checking fails, our tool examines a set of counterexamples to safety/liveness properties to generate constraints on unknown functions that must be satisfied by subsequent completions. For evaluation, we show that our prototype is able to automatically discover interesting missing details in distributed protocols for mutual exclusion, self stabilization, and cache coherence.
Scenarios, or Message Sequence Charts, offer an intuitive way of describing the desired behaviors of a distributed protocol. In this paper we propose a new way of specifying finite-state protocols using scenarios: we show that it is possible to autom
atically derive a distributed implementation from a set of scenarios augmented with a set of safety and liveness requirements, provided the given scenarios adequately emph{cover} all the states of the desired implementation. We first derive incomplete state machines from the given scenarios, and then synthesis corresponds to completing the transition relation of individual processes so that the global product meets the specified requirements. This completion problem, in general, has the same complexity, PSPACE, as the verification problem, but unlike the verification problem, is NP-complete for a constant number of processes. We present two algorithms for solving the completion problem, one based on a heuristic search in the space of possible completions and one based on OBDD-based symbolic fixpoint computation. We evaluate the proposed methodology for protocol specification and the effectiveness of the synthesis algorithms using the classical alternating-bit protocol.
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide n
ew temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a within modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.
