T-systems are generalisations of marked graph Petri nets. This paper describes synthesis algorithms that allow bounded or unbounded T-systems to be derived from finite or infinite labelled transition systems satisfying a set of necessary properties. These properties can thus be interpreted as axioms characterising T-system state spaces.

We use the by now well established setting of modal semirings to derive a modal algebra for Petri nets. It is based on a relation-algebraic calculus for separation logic that enables calculations of properties in a pointfree fashion and at an abstract level. Basically, we start from an earlier logical approach to Petri nets that in particular uses modal box and diamond operators for stating properties about the state space of such a net. We provide relational translations of the logical formulas which further allow the characterisation of general behaviour of transitions in an algebraic fashion. From the relational structure an algebra for frequently used properties of Petri nets is derived. In particular, we give connections to typical used assertion classes of separation logic. Moreover, we demonstrate applicability of the algebraic approach by calculations concerning a standard example of a mutex net.

The logic PML is a probabilistic version of Hennessy---Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal nondeterminism. In this paper, two alternative interpretations of PML over nondeterministic and probabilistic processes as models are considered, and two new bisimulation-based equivalences that are in full agreement with those interpretations are provided. The new equivalences include as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead known to agree with two versions of Hennessy---Milner logic extended with an additional probabilistic operator interpreted over state distributions in place of individual states. The new interpretations of PML and the corresponding new bisimilarities are thus the first ones to offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or that mix nondeterminism and probability in an alternating/nonalternating way.

In this paper we recast the classical Darondeau---Degano's causal semantics of concurrency in a coalgebraic setting, where we derive a compact model. Our construction is inspired by the one of Montanari and Pistore yielding causal automata, but we show that it is instance of an existing categorical framework for modeling the semantics of nominal calculi, whose relevance is further demonstrated. The key idea is to represent events as names, and the occurrence of a new event as name generation. We model causal semantics as a coalgebra over a presheaf, along the lines of the Fiore---Turi approach to the semantics of nominal calculi. More specifically, we take a suitable category of finite posets, representing causal relations over events, and we equip it with an endofunctor that allocates new events and relates them to their causes. Presheaves over this category express the relationship between processes and causal relations among the processes' events. We use the allocation operator to define a category of well-behaved coalgebras: it models the occurrence of a new event along each transition. Then we turn the causal transition relation into a coalgebra in this category, where labels only exhibit maximal events with respect to the source states' poset, and we show that its bisimilarity is essentially Darondeau---Degano's strong causal bisimilarity. This coalgebra is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, where states only retain the poset of the most recent events for each atomic subprocess, and are isomorphic up to order-preserving permutations. Remarkably, this reduction of states is automatically performed along the equivalence.

Regular expressions (RE) are an algebraic formalism for expressing regular languages, widely used in string search and as a specification language in verification. In this paper, we introduce and i...

In this paper we study the construction and the enumeration of binary words in $$\{0,1\}^*$$ having more 1's than 0's and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1's than 0's and then kills those containing the forbidden patterns. Finally, we give the generating function of such words according to the number of ones.

In this paper we propose a generalization of the accepting splicing systems introduced in Mitrana et al. (Theor Comput Sci 411:2414–2422, 2010). More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word is rejected if either no permitting word is ever generated (like in Mitrana et al. in Theor Comput Sci 411:2414–2422, 2010) or a forbidding word has been generated and no permitting word had been generated before. We investigate the computational power of the new variants of accepting splicing systems and the interrelationships among them. We show that the new condition strictly increases the computational power of accepting splicing systems. Although there are regular languages that cannot be accepted by any of the splicing systems considered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of (extended) finite splicing systems without additional restrictions. We also show that the smallest class of languages out of the four classes defined by accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediately derived from the proof of this result.

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to word bounded languages, this class coincides with the class of semilinear languages. We also study the closure properties of the classes of languages definable in FO[+1], FO[<], FO[+] and FOC[+] under the main classical operations.

Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch arrivals, batch services, autocorrelation of inter-arrival times, and autocorrelation of batch sizes can be accommodated in the queue, by a suitable use of Markov modulation and generalized exponential distribution. The queue has a provision for negative customers too. Transformations of the balance equations into a computable form are proposed in order to obtain the steady state probabilities with the Spectral Expansion method. This queue is used to model the High Speed Downlink Packet Access (HSDPA) wireless networks. The model is an integrated one with respect to HSDPA, capable of accommodating many of the intricate aspects of HSDPA such as, channel allocation policy, loss of packets due to channel fading, bursty and correlated traffic. Good agreement is observed between the numerical results of the proposed analytical model and those of an independent simulator of real HSDPA and radio channel behaviors. The comparison of the terminal categories specified by the 3rd Generation Partnership Project (3GPP) is also presented.

In this note, we show that the number of equivalence queries asked by an algorithm proposed in Becerra-Bonache et al. (Proceedings of the 8th International Colloquium on Grammatical Inference (ICGI ’06), Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin 2006) that learns deterministic finite automata with correction and equivalence queries is at most the injectivity degree of the target language, a notion that corresponds to the number of repetitions among the correcting words of all the elements in the quotient of that language by the Myhill-Nerode equivalence. Further, we propose a tight upper bound for the number of correction queries as a function which depends on the index of the target language, the length of the longest counterexample returned by the teacher and the injectivity degree of the target language. However, the bounds obtained here for the number of CQs are optimal for the LCA algorithm, and they do not represent a tight upper bound for DFA learning with EQs and CQs in general.