## Section: New Results

### Foundations of Concurrency

Distributed systems have changed substantially in the recent past with the
advent of phenomena like social networks and cloud computing. In the previous
incarnation of distributed computing the emphasis was on consistency, fault
tolerance, resource management and related topics; these were all characterized
by *interaction between processes*. Research proceeded along two lines: the
algorithmic side which dominated the Principles Of Distributed Computing
conferences and the more process algebraic approach epitomized by CONCUR where
the emphasis was on developing compositional reasoning principles. What marks
the new era of distributed systems is an emphasis on managing access to
information to a much greater degree than before.

#### An Algebraic View of Space/Belief and Extrusion/Utterance for Concurrency/Epistemic Logic

The notion of constraint system (cs) is central to declarative formalisms from concurrency theory such as process calculi for concurrent constraint programming (ccp). Constraint systems are often represented as lattices: their elements, called constraints, represent partial information and their order corresponds to entailment. Recently a notion of n-agent spatial cs was introduced to represent information in concurrent constraint programs for spatially distributed multi-agent systems. From a computational point of view a spatial constraint system can be used to specify partial information holding in a given agent's space (local information). From an epistemic point of view a spatial cs can be used to specify information that a given agent considers true (beliefs). Spatial constraint systems, however, do not provide a mechanism for specifying the mobility of information/processes from one space to another. Information mobility is a fundamental aspect of concurrent systems.

In the poster paper [24] we discussed using constraint systems with an algebraic operator that correspond to moving information in-between spaces as to mimic the mobility of data of distributed systems such as posting opinions/lies to other spaces or publicly disclosing data. In the conference paper [22] we enriched spatial constraint systems with operators to specify information and processes moving from a space to another. We referred to these news structures as spatial constraint systems with extrusion. We investigated the properties of this new family of constraint systems and illustrated their applications. From a computational point of view the new operators provide for process/information extrusion, a central concept in formalisms for mobile communication. From an epistemic point of view extrusion corresponds to a notion we called utterance; a piece of information that an agent communicates to others but that may be inconsistent with the agent’s beliefs. Utterances can then be used to express instances of epistemic notions, which are commonplace in social media, such as hoaxes or intentional lies. Spatial constraint systems with extrusion can be seen as complete Heyting algebras equipped with maps to account for spatial and epistemic specifications. In the journal paper [28] we extended our work in [22] by showing that spatial constraint systems can also express the epistemic notion of knowledge by means of a derived spatial operator that specifies global information.

#### A Labelled Semantics for Soft Concurrent Constraint Programming

In [21] we presented a labelled semantics for Soft Concurrent Constraint Programming (SCCP), a language where concurrent agents may synchronize on a shared store by either posting or checking the satisfaction of (soft) constraints. SCCP generalizes the classical formalism by parametrising the constraint system over an order-enriched monoid: the monoid operator is not required to be idempotent, thus adding the same information several times may change the store. The novel operational rules are shown to offer a sound and complete co-inductive technique to prove the original equivalence over the unlabelled semantics.

#### Verification methods for concurrent Constraint Programming

Concurrent Constraint Programming (CCP) is a well-established declarative framework from concurrency theory. Its foundations and principles e.g., semantics, proof systems, axiomatizations, have been thoroughly studied for over the last two decades. In contrast, the development of algorithms and automatic verification procedures for CCP have hitherto been far too little considered.

To the best of our knowledge there is only one existing verification algorithm for the standard notion of CCP program (observational) equivalence. In [16] we first showed that this verification algorithm has anexponential-time complexity even for programs from a representative sub-language of CCP; the summation-free fragment ( CCP+). We then significantly improved on the complexity of this algorithm by providing two alternative polynomial-time decision procedures for CCP+ program equivalence. Each of these two procedures has an advantage over the other. One has a better time complexity. The other can be easily adapted for the full language of CCP to produce significant state space reductions. The relevance of both procedures derives from the importance of CCP+. This fragment, which has been the subject of many theoretical studies, has strong ties to first-order logic and an elegant denotational semantics, and it can be used to model real-world situations. Its most distinctive feature is that of confluence, a property we exploit to obtain our polynomial procedures.

Bisimilarity is a standard behavioral equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for CCP, and a CCP partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimilarity is a central behavioral equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milner's reduction from weak to strong bisimilarity; a technique referred to as saturation. In [15] we demonstrated that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for CCP. We also gave an alternative reduction from weak CCP bisimilarity to the strong one that allows us to use the CCP partition refinement algorithm for deciding this equivalence. We also proved that due to distinctive nature of CCP, the new method does not introduce infinitely-branching in the resulting transition systems. Finally, we derived an algorithm to automatically verify the notion of weak bisimilarity in CCP.

The ntcc calculus extends CCP with the notion of discrete time-units for the specification of reactive systems. Moreover, ntcc features constructors for non-deterministic choices and asynchronous behavior, thus allowing for (1) synchronization of processes via constraint entailment during a time-unit and (2) synchronization of processes along time-intervals. In [20] we developed the techniques needed for the automatic verification of ntcc programs based on symbolic model checking. We showed that the internal transition relation, modeling the behavior of processes during a time-unit (1 above), could be symbolically represented by formulas in a suitable fragment of linear time temporal logic. Moreover, by using standard techniques as difference decision diagrams, we provided a compact representation of these constraints. Then, relying on a fixpoint characterization of the timed constructs, we obtained a symbolic model of the observable transition (2 above). We proved that our construction is correct with respect to the operational semantics. Finally, we introduced a prototypical tool implementing our method.