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Register a new userType-checking Liveness for Collaborative Processes with Bounded and Unbounded Recursion
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We present the first session typing system guaranteeing request-response liveness properties for possibly non-terminating communicating processes. The types augment the branch and select types of the standard binary session types with a set of required responses, indicating that whenever a particular label is selected, a set of other labels, its responses, must eventually also be selected. We prove that these extended types are strictly more expressive than standard session types. We provide a type system for a process calculus similar to a subset of collaborative BPMN processes with internal (data-based) and external (event-based) branching, message passing, bounded and unbounded looping. We prove that this type system is sound, i.e., it guarantees request-response liveness for dead-lock free processes. We exemplify the use of the calculus and type system on a concrete example of an infinite state system.
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We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.
In the design of probabilistic timed systems, bounded requirements concerning behaviour that occurs within a given time, energy, or more generally cost budget are of central importance. Traditionally, such requirements have been model-checked via a reduction to the unbounded case by unfolding the model according to the cost bound. This exacerbates the state space explosion problem and significantly increases runtime. In this paper, we present three new algorithms to model-check time- and cost-bounded properties for Markov decision processes and probabilistic timed automata that avoid unfolding. They are based on a modified value iteration process, on an enumeration of schedulers, and on state elimination techniques. We can now obtain results for any cost bound on a single state space no larger than for the corresponding unbounded or expected-value property. In particular, we can naturally compute the cumulative distribution function at no overhead. We evaluate the applicability and compare the performance of our new algorithms and their implementation on a number of case studies from the literature.
Timed Automata (TA) are a very popular modeling formalism for systems with time-sensitive properties. A common task is to verify if a network of TA satisfies a given property, usually expressed in Linear Temporal Logic (LTL), or in a subset of Timed Computation Tree Logic (TCTL). In this paper, we build upon the TACK bounded model checker for TA, which supports a signal-based semantics of TA and the richer Metric Interval Temporal Logic (MITL). TACK encodes both the TA network and property into a variant of LTL, Constraint LTL over clocks (CLTLoc). The produced CLTLoc formula can then be solved by tools such as Zot, which transforms CLTLoc properties into the input logics of Satisfiability Modulo Theories (SMT) solvers. We present a novel method that preserves TACKs encoding of MITL properties while encoding the TA network directly into the SMT solver language, making use of both the BitVector logic and the logic of real arithmetics. We also introduce several optimizations that allow us to significantly outperform the CLTLoc encoding in many practical scenarios.
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the algorithm; and get as a corollary the injectivity of type constructors. Then we give the definition of a correct and complete type-checking algorithm for terms in normal form. We extend the results to proof-irrelevant propositions.
Ong has shown that the modal mu-calculus model checking problem (equivalently, the alternating parity tree automaton (APT) acceptance problem) of possibly-infinite ranked trees generated by order-n recursion schemes is n-EXPTIME complete. We consider two subclasses of APT and investigate the complexity of the respective acceptance problems. The main results are that, for APT with a single priority, the problem is still n-EXPTIME complete; whereas, for APT with a disjunctive transition function, the problem is (n-1)-EXPTIME complete. This study was motivated by Kobayashis recent work showing that the resource usage verification of functional programs can be reduced to the model checking of recursion schemes. As an application, we show that the resource usage verification problem is (n-1)-EXPTIME complete.
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