Abstract Session-based concurrencyis a type-based approach to the analysis of message-passing programs. These programs may be specified in anoperationalordeclarativestyle: the former defines how interactions are properly structured; the latter defines governing conditions for correct interactions. In this paper, we study rigorous relationships between operational and declarative models of session-based concurrency. We develop a correct encoding of session $$\pi $$ π -calculus processes into the linear concurrent constraint calculus ( $$\texttt {lcc}$$ lcc ), a declarative model of concurrency based on partial information (constraints). We exploit session types to ensure that our encoding satisfies precise correctness properties and that it offers a sound basis on which operational and declarative requirements can be jointly specified and reasoned about. We demonstrate the applicability of our results by using our encoding in the specification of realistic communication patterns with time and contextual information.

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide algorithms that compute the distributive group information of finite groups.

This issue of Mathematical Structures in Computer Science (MSCS) contains a selection of papers presented at the 12th International Colloquium on Theoretical Aspects of Computing (ICTAC 2015), which took place in Cali, Colombia, on October 29–31, 2015.

Abstract A recent trend in object-oriented programming languages is the use of access permissions (APs) as an abstraction for controlling concurrent executions of programs. The use of AP source code annotations defines a protocol specifying how object references can access the mutable state of objects. Although the use of APs simplifies the task of writing concurrent code, an unsystematic use of them can lead to subtle problems. This paper presents a declarative interpretation of APs as linear concurrent constraint programs (lcc). We represent APs as constraints (i.e., formulas in logic) in an underlying constraint system whose entailment relation models the transformation rules of APs. Moreover, we use processes inlccto model the dependencies imposed by APs, thus allowing the faithful representation of their flow in the program. We verify relevant properties about AP programs by taking advantage of the interpretation oflccprocesses as formulas in Girard's intuitionistic linear logic (ILL). Properties include deadlock detection, program correctness (whether programs adhere to their AP specifications or not), and the ability of methods to run concurrently. By relying on a focusing discipline for ILL, we provide a complexity measure for proofs of the above-mentioned properties. The effectiveness of our verification techniques is demonstrated by implementing the Alcove tool that includes an animator and a verifier. The former executes thelccmodel, observing the flow of APs, and quickly finding inconsistencies of the APs vis-à-vis the implementation. The latter is an automatic theorem prover based on ILL.

Session-based concurrency is a type-based approach to the analysis of communication-intensive systems. Correct behavior in these systems may be specified in an operational or declarative style: the former defines how interactions are structured; the latter defines governing conditions. In this paper, we investigate the relationship between operational and declarative models of session-based concurrency. We propose two interpretations of session π-calculus processes as declarative processes in linear concurrent constraint programming (lcc). They offer a basis on which both operational and declarative requirements can be specified and reasoned about. By coupling our interpretations with a type system for lcc, we obtain robust declarative encodings of π-calculus mobility.

We enrich spatial constraint systems with operators to specify information and processes moving from a space to another. We shall refer to these news structures as spatial constraint systems with extrusion. We shall investigate the properties of this new family of constraint systems and illustrate 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 shall call 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 common place 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.

A recent trend in object oriented programming languages is the use Access Permissions (AP) as abstraction to control concurrent executions. AP define a protocol specifying how different references can access the mutable state of objects. Although AP simplify the task of writing concurrent code, an unsystematic use of permissions in the program can lead to subtle problems. This paper presents a Linear Concurrent Constraint (lcc) approach to verify AP annotated programs. We model AP as constraints (i.e., formulas in logic) in an underlying constraint system, and we use entailment of constraints to faithfully model the flow of AP in the program. We verify relevant properties about programs by taking advantage of the declarative interpretation of lcc agents as formulas in linear logic. Properties include deadlock detection, program correctness (whether programs adhere to their AP specifications or not), and the ability of methods to run concurrently. We show that those properties are decidable and we present a complexity analysis of finding such proofs. We implemented our verification and analysis approach as the Alcove tool, which is available on-line.