Context-Sensitive String Languages and Recognizable Picture Languages

The theorem stating that the family of frontiers of recognizable tree languages is exactly the family of context-free languages (see J. Mezei and J. B. Wright, 1967,Inform. and Comput.11, 3–29), is a basic result in the theory of formal languages. In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of context-sensitive languages     

Trace,failure and testing equivalences for communicating processes

A basic question in the theory of communicating processes is “When should two processes be considered equivalent?”. Attempts to answer this question have led to the concepts of observation equivalence, bisimulations, testing equivalence, failure equivalence, etc. The main point of this paper is to increase the understanding and motivation for two of these equivalences, namely failure and testing equivalences. The approach starts with the idea that the equivalence of processes should be reducible to the visible sequences of actions which a process performs in various contexts. This idea is implemented by a string-based semantic order for communicating processes where divergence is catastrophic. Under some assumptions about contexts, the resulting semantics is shown to be equivalent to theimproved failure semantics of Brookes and Roscoe⁽¹⁾ and also to themust testing-semantics of Hennessy and DeNicola.^(2–4) This characterization gives independent support for the appropriateness of failures and testing.     

On a boundary value method for computing Sturm–Liouville potentials from two spectra

Convergence of a boundary value method (BVM) in Aceto et al. [Boundary value methods for the reconstruction of Sturm–Liouville potentials, Appl. Math. Comput. 219 (2012), pp. 2960–2974] for computing Sturm–Liouville potentials from two spectra is discussed. In Aceto et al. (2012), a continuous approximation of the unknown potential belonging to a suitable function space of finite dimension is obtained by forming an associated set of nonlinear equations and solving these with a quasi-Newton approach. In our paper, convergence of the quasi-Newton approach is established and convergence of the estimate of the unknown potential, provided by the exact solution of the nonlinear equation, to the true potential is proved. To further investigate the properties of the BVM in Aceto et al. (2012), some other spaces of functions are introduced. Numerical examples confirm the theoretically predicted convergence properties and show the accuracy and stability of the BVM.     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.     

Can LCF be topped? Flat lattice models of typed λ-calculus

Plotkin ((1977) Theoret. Comput. Sci. 5: 223–256) examines the denotational semantics of PCF (essentially typed λ-calculus with arithmetic and looping). The standard Scott semantics V is computationally adequate but not fully abstract; with the addition of some parallel facilities, it becomes fully abstract, and with the addition of an existential operator, denotationally universal. We consider carrying out the same program for , the Scott models built from flat lattices rather than flat cpo's. Surprisingly, no computable extension of PCF can be denotationally universal; perfectly reasonable semantic values such as supremum and Plotkin's “parallel or” cannot be definable. There is an unenlightening fully abstract extension _A (approx), based on Gödel numbering and syntactic analysis. Unfortunately, this is the best we can do; operators defined by PCF-style rules cannot give a fully abstract language. (There is a natural and desirable property, operational extensionality, which prevents full abstraction with respect to .) However, we show that Plotkin's program can be carried out for a nonconfluent evaluator.     

A Coinduction Principle for Recursive Data Types Based on Bisimulation

The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result (in the sense of S. Abramsky and C.-H. L. Ong [Inform. and Comput.105, 159–267 (1993)] for the canonical model of the untyped call-by-valueλ-calculus is proved. Also, the operational notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.     

Complexity of reachability problems for finite discrete dynamical systems

Sequential Dynamical Systems (SDSs) are a special type of finite discrete dynamical systems that can be used to model simulation systems. We focus on the computational complexity of testing several phase space properties of SDSs. Our main result is a sharp delineation between classes of SDSs whose behavior is easy to predict and those whose behavior is hard to predict. Specifically, we show the following.

1.

Several state reachability problems for SDSs are PSPACE-complete, even when restricted to SDSs whose underlying graphs are of bounded bandwidth (and hence of bounded pathwidth and treewidth), and the function associated with each node is symmetric. Moreover, this result holds even when the underlying graph is d-regular for some constant d and all the nodes compute the same symmetric Boolean function. An immediate corollary of this result is a PSPACE-hard lower bound on the complexity of reachability problems for regular generalized 1D-Cellular Automata and undirected systolic networks with Boolean totalistic local transition functions.

2.

In contrast, the above reachability problems are solvable in polynomial time for SDSs when the Boolean function associated with each node is symmetric and monotone.

The PSPACE-completeness results follow as corollaries of simulation results which show for several classes of SDSs, how one class of SDSs can be efficiently simulated by another (more restricted) class of SDSs. We also prove several structural properties concerning the phase space of an SDS. SDSs are closely related to Cellular Automata (CA), concurrent transition systems, discrete Hopfield networks and systolic networks. This observation in conjunction with our lower bounds for SDSs, yields new PSPACE-hard lower bounds on the complexity of state reachability problems for these models, extending some of the earlier results in [K. Culik II, J. Karhumäki, On totalistic systolic networks, Inform. Process. Lett. 26 (5) (1988) 231-236; P. Floréen, E. Goles, G. Weisbuch, Transient length in sequential iterations of threshold functions, Discrete Appl. Math. 6 (1983) 95-98; P. Floréen, P. Orponen, Complexity issues in discrete Hopfield networks, Research Report No. A-1994-4, Department of Computer Science, University of Helsinki, 1994. Also appears in: I. Parberry (Ed.), Comp. and Learning Complexity of Neural Networks: Advanced Topics, 1999; D. Harel, O. Kupferman, M.Y. Vardi, On the complexity of verifying concurrent transition systems, Inform. and Comput. 173 (2002) 143-161; S.K. Shukla, H.B. Hunt III, D.J. Rosenkrantz, R.E. Stearns, On the complexity of relational problems for finite state processes, in: International Colloquium on Automata Programming and Languages, ICALP, 1996, pp. 466-477; A. Rabinovich, Complexity of equivalence problems for concurrent systems of finite agents, Inform. and Comput. 127 (2) (1997) 164-185].     

Testing Preorders for Probabilistic Processes

We present a testing preorder for probabilistic processes based on a quantification of the probability with which processes pass tests. The theory enjoys close connections with the classical testing theory of De Nicola and Hennessy in that whenever a process passes a test with probability 1 (respectively some nonzero probability) in our setting, then the process must (respectively may) pass the test in the classical theory. We also develop an alternative characterization of the probabilistic testing preorders that takes the form of a mapping from probabilistic traces to the interval [0, 1], where a probabilistic trace is an alternating sequence of actions and probability distributions over actions. Finally, we give proof techniques, derived from the alternative characterizations, for establishing preorder relationships between probabilistic processes. The utility of these techniques is demonstrated by means of some simple examples.     

Refusal testing

When manipulating concurrent processes it is desirable to suppress their internal details and to consider two processes to be equivalent if their external behaviours are equivalent. Following Milner and De Nicola & Hennessy we take this external equivalence to mean that an observer cannot tell the processes apart by testing their responses to the same stimuli. We introduce a form of testing (refusal testing) which is more powerful than that of De Nicola & Hennessy in that the observer not only tests whether a process will perform an action but is also allowed under certain circumstances to discover in a finite amount of time that the process will not perform an action. The equivalence associated with refusal testing is compared with De Nicola & Hennessy's testing equivalence and Milner's observation equivalence, and a sound and complete proof system is provided for refusal equivalence when applied to CCS processes.     

A Dynamic Logic of Agency II: Deterministic $${\mathcal{DLA}}$$ , Coalition Logic,and Game Theory

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called DDLA{\mathcal{DDLA}} (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In DDLA{\mathcal{DDLA}} it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess DDLA{\mathcal{DDLA}} we prove that it embeds Coalition Logic. We then extend DDLA{\mathcal{DDLA}} with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium.     

Asynchronous Mappings and Asynchronous Cellular Automata

The aim of this paper is the study of asynchronous automata, a special kind of automata which encode the independency relation between actions and which enable their concurrent execution. These automata, introduced by Zielonka (RAIRO Inform. Theor. Appl.21, 99-135 (1987)), constitute a natural extension of finite automata to the case of asynchronous parallelism. Their behaviour is described by trace languages, subsets of partially commutative monoids. The main result concerning this class of automata states that they accept exactly all recognizable trace languages. In this paper we give new improved constructions of asynchronous automata. In the final part of the paper we present a distributed system of messages with bounded time-stamps based on asynchronous automata.     

Broadcast Calculus Interpreted in CCS upto Bisimulation

A function M is given that takes any process p in the calculus of broadcasting systems CBS and returns a CCS process M(p) with special actions {hear?, heard!, say?, said!} such that a broadcast of ω by p is matched by the sequence say? τ^* said(ω) by M(p) and a reception of υ by hear(v) τ^*heard!. It is shown that p M(p), where is a bisimulation equivalence using the above matches, and that M(p) has no CCS behaviour not covered by . Thus the abstraction of a globally synchronising broadcast can be implemented by sequences of local synchronisations. The criteria of correctness are unusual, and arguably stronger than requiring equivalences to be preserved — the latter does not guarantee that meaning is preserved. Since is not a native CCS equivalence, it is a matter of dicussion what the result says about Holmer's (CONCUR'93) conjecture, partially proved by Ene and Muntean (FCT'99), that CCS cannot interpret CBS upto preservation of equivalence.     

Exploring probabilistic bisimulations, part I

We take a fresh look at strong probabilistic bisimulations for processes which exhibit both non-deterministic and probabilistic behaviour. We suggest that it is natural to interpret such processes as distributions over states in a probabilistic labelled transition system, a pLTS; this enables us to adapt the standard notion of contextual equivalence to this setting. We then prove that a novel form of bisimulation equivalence between distributions are both sound and complete with respect to this contextual equivalence. We also show that a very simple extension to HML, Hennessy–Milner Logic, provides finite explanations for inequivalences between distributions. Finally we show that our bisimulations between distributions in a pLTS are simply an alternative characterisation of a standard notion of probabilistic bisimulation equivalence, defined between states in a pLTS.     

On the Correctness of Goscinski′s Algorithm

In this paper, the correctness of the mutual exclusion algorithm proposed by Goscinski (J. Parallel Distribut. Comput.9(7), 77-82 (1990)), hereafter , is discussed and its features are compared with other token-based algorithms already published. In particular, we show that works correctly only using a communication system that guarantees a total ordering of messages, otherwise it is incorrect. We further give a modified version of , hereafter , and show that is actually a simple modification of the Suzuki-Kasami algorithm (ACM Trans. Comput. Systems3(5), 344-349 (1985)).     

Ready to preorder: The case of weak process semantics

Recently, Aceto, Fokkink and Ingólfsdóttir proposed an algorithm to turn any sound and ground-complete axiomatisation of any preorder listed in the linear time-branching time spectrum at least as coarse as the ready simulation preorder, into a sound and ground-complete axiomatisation of the corresponding equivalence—its kernel. Moreover, if the former axiomatisation is ω-complete, so is the latter. Subsequently, de Frutos Escrig, Gregorio Rodríguez and Palomino generalised this result, so that the algorithm is applicable to any preorder at least as coarse as the ready simulation preorder, provided it is initials preserving. The current paper shows that the same algorithm applies equally well to weak semantics: the proviso of initials preserving can be replaced by other conditions, such as weak initials preserving and satisfying the second τ-law. This makes it applicable to all 87 preorders surveyed in “the linear time-branching time spectrum II” that are at least as coarse as the ready simulation preorder. We also extend the scope of the algorithm to infinite processes, by adding recursion constants. As an application of both extensions, we provide a ground-complete axiomatisation of the CSP failures equivalence for BCCS processes with divergence.     

Weakly distributive domains(Ⅱ)

In our previous work (Inform. and Comput., 2005, 202: 87–103), we have shown that for any ω-algebraic meet-cpo D, if all higher-order stable function spaces built from D are ω-algebraic, then D is finitary. This accomplishes the first of a possible, two-step process in solving the problem raised (LNCS, 1991, 530: 16–33; Domains and lambda-calculi, Cambridge Univ. Press, 1998) whether the category of stable bifinite domains of Amadio-Droste-G?bel (LNCS, 1991, 530: 16–33; Theor. Comput. Sci., 1993, 111: 89–101) is the largest cartesian closed full subcategory within the category of ω-algebraic meet-cpos with stable functions. This paper presents the results of the second step, which is to show that for any ω-algebraic meet-cpo D satisfying axioms M and I to be contained in a cartesian closed full sub-category using ω-algebraic meet-cpos with stable functions, it must not violate MI^∞. We introduce a new class of domains called weakly distributive domains and show that for these domains to be in a cartesian closed category using ω-algebraic meet-cpos, property MI^∞ must not be violated. Further, we demonstrate that principally distributive domains (those for which each principle ideal is distributive) form a proper subclass of weakly distributive domains, and Birkhoff’s M ₃ and N ₅ (Introduction to Lattices and order, Cambridge Univ. Press, 2002) are weakly distributive (but non-distributive). Then, we establish characterization results for weakly distributive domains. We also introduce the notion of meet-generators in constructing stable functions and show that if an ω-algebraic meet-cpo D contains an infinite number of meet-generators, then [D → D] fails I. However, the original problem of Amadio and Curien remains open.     

On Performance Congruences for Process Algebras

Based on the hypothesis of durational actions and process synchronization with “busy waiting” mechanism,performance equivalencehas been proposed to introduce a simple form of performance evaluation in process algebras. This equivalence enjoys many of the pleasant properties of those in the untimed setting but it is not a congruence for parallel composition with synchronization. In this paper we give a bisimulation-based characterization of the coarsest congruence contained within performance equivalence (and discuss alternative formulations). This problem was left open in several papers. We study how the new equivalence, calledperformance congruence, relates with other closed equivalences in the literature and show that, unlike other proposals, it is a natural extension of those standard in the untimed setting. The weak version of performance congruence, which abstracts from internal details, is also studied. A number of examples of processes related or taken apart by performance congruence, and its weak version, are provided. A nontrivial one is also presented to illustrate the utility of the new congruences. The paper concludes with further observations concerning performance congruence and with a discussion on related and further interesting work.     

Hardness of equivalence checking for composed finite-state systems

Computational complexity of comparing behaviours of systems composed from interacting finite-state components is considered. The main result shows that the respective problems are EXPTIME-hard for all relations between bisimulation equivalence and trace preorder, as conjectured by Rabinovich (Inf Comput 139(2):111–129, 1997). The result is proved for a specific model of parallel compositions where the components synchronize on shared actions but it can be easily extended to other similar models,   to labelled 1-safe Petri nets. Further hardness results are shown for special cases of acyclic systems.     

A Worst-Case Analysis of the LZ2 Compression Algorithm

Sheinwald, Lempel, and Ziv (1995,Inform. and Comput.116, 128–133) proved that the power of off-line coding is not useful if we want on-line decodable files, as far as asymptotical results are concerned. In this paper, we are concerned with the finite case and consider the notion of on-line decodable optimal parsing based on the parsing defined by the Ziv–Lempel (LZ2) compression algorithm. De Agostino and Storer (1996,Inform. Process. Lett.59, 169–174) proved the NP-completeness of computing the optimal parsing and that a sublogarithmic factor approximation algorithm cannot be realized on-line. We show that the Ziv–Lempel algorithm and two widely used practical implementations produce an O(n^1/4) approximation of the optimal parsing, wherenis the length of the string. By working with de Bruijn sequences, we show also infinite families of binary strings on which the approximation factor isΘ(n^1/4).