De Morgan Dual Nominal Quantifiers Modelling Private Names in Non-Commutative Logic

This paper explores the proof theory necessary for recommending an expressive but decidable first-order system, named MAV1, featuring a de Morgan dual pair of nominal quantifiers. These nominal quantifiers called `new' and `wen' are distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers. The novelty of these nominal quantifiers is they are polarised in the sense that `new' distributes over positive operators while `wen' distributes over negative operators. This greater control of bookkeeping enables private names to be modelled in processes embedded as formulae in MAV1. The technical challenge is to establish a cut elimination result, from which essential properties including the transitivity of implication follow. Since the system is defined using the calculus of structures, a generalisation of the sequent calculus, novel techniques are employed. The proof relies on an intricately designed multiset-based measure of the size of a proof, which is used to guide a normalisation technique called splitting. The presence of equivariance, which swaps successive quantifiers, induces complex inter-dependencies between nominal quantifiers, additive conjunction and multiplicative operators in the proof of splitting. Every rule is justified by an example demonstrating why the rule is necessary for soundly embedding processes and ensuring that cut elimination holds.Comment: Submitted for review 18/2/2016; accepted CONCUR 2016; extended version submitted to journal 27/11/201

Mutual Mobile Membranes Systems with Surface Objects

In this paper we introduce mutual mobile membranes with surface objects, systems which have biological motivation. In P systems with mobile membranes with surface objects, a membrane may enter or exit another membrane. The second membrane just undergoes the action, meaning that it has no control on when the movement takes place. This kind of movement illustrates the lack of an agreement (synchronization) similar to an asynchronous evolution. In mutual mobile membranes with surface objects this aspect is adjusted: any movement takes place only if both participants agree by synchronizing their evolution. In membranes two kinds of competition can occur: resource competition and location competition. Resource competition refers to rules which request the same resources, and the available resources can only be allocated to some of the rules. Location competition refers to the movement of a membrane in the hierarchical structure of the membrane systems under the request of some conflict rules.We use the two variants of membrane systems in order to describe and explain these kinds of competition, and introduce synchronizing objects in mutual mobile membranes which will help to solve the resource and location competitions

Solving SAT with Active Membranes and Pre-Computed Initial Con gurations

In this paper we provide algorithms for solving the SAT problem using P systems with active membranes with neither polarization nor division rules. The semi- uniform solutions are given under the assumption that initial con gurations (either al- phabet or structure) of exponential size are pre-computed by well-de ned P systems (P systems with replicated rewriting and P systems with active membranes and membrane creation, respectively) working in polynomial time. An important observation is that we specify how the pre-computed initial con gurations are constructed

Life-Death Ratio Approach by a Multiset-Based Type System

We introduce and study a multiset-based type system with ratio thresholds motivated by an important regulatory mechanism inside a cell which try to maintain a \life-death" ratio between some given lower and upper thresholds. We use such a type system to control ratio thresholds in a bio-inspired and multisets-based formalism. For this type system we prove a subject reduction theorem, together with soundness and completeness theorems. A type inference for deducing the type of a system is presented

Verifying P Systems with Costs by Using Priced-Timed Maude

We consider P systems that assigns storage costs per step to membranes, and execution costs to rules. We present an abstract syntax of the new class of membrane systems, and then deal with costs by extending the operational semantics of P systems with promoters, inhibitors and registers.We use Priced-Timed Maude to implement the P systems with costs. By using such a rewriting engine which corresponds to the semantics of membrane systems with costs, we are able to prove the operational correctness of this implementation. Based on such an operational correspondence, we can analyze properly the evolutions of the P systems with costs, and verify several reachability properties, including the cost of computations that reach a given membrane con guration. This approach opens the way to various optimization problems related to membrane systems, problems making sense in a bio-inspired model which now can be veri ed by using a complex software platform