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In recent work we have proposed a novel approach to define idealized
type systems for object-oriented languages, based on abstract compilation of
programs into Horn formulas which are interpreted w.r.t. the coinductive (that is, the greatest) Herbrand model. In this paper we investigate how this approach can be applied also in
the presence of imperative features.
This is made possible by considering a natural translation of Static Single Assignment intermediate form programs into Horn formulas, where φ functions
correspond to union types.
The calculus of looping sequences is a formalism for describing the
evolution of biological systems by means of term rewriting rules. In
this paper we enrich this calculus with a type discipline which
preserves some biological properties depending on the minimum and
the maximum number of elements of some type requested by the present elements. The type
system enforces these properties and typed reductions guarantee that
evolution preserves them. As an example, we model the hemoglobin
structure and the equilibrium between cell death and division: typed
reductions prevent undesirable behaviors.
Minimizing a deterministic finite automata (DFA) is a very important problem in theory of automata and formal languages.
Hopcroft's algorithm represents the fastest known solution to the such a problem. In this paper we analyze the behavior of this algorithm on a family binary automata, called tree-like automata, associated to binary labeled trees constructed by words. We prove that all the executions of the algorithm on tree-like automata associated to trees, constructed by standard words, have running time with the same asymptotic growth rate. In particular, we provide a lower and upper bound for the running time of the algorithm expressed in terms of combinatorial properties of the trees. We consider also tree-like automata associated to trees constructed by de Brujin words,
and we prove that a queue implementation of the waiting set gives a Θ(n log n) execution while a stack implementation produces a linear execution. Such a result confirms the conjecture given in [A. Paun, M. Paun and A. Rodríguez-Patón.
Theoret. Comput. Sci.410 (2009) 2424–2430.] formulated for a family of unary automata and, in addition, gives a positive answer also for the binary case.
An ever present, common sense idea in language modelling research is that, for a
word to be a valid phrase, it should comply with multiple constraints at
once. A new language definition model is studied, based on agreement or consensus
between similar strings. Considering a regular set of strings over a bipartite
alphabet made by pairs of unmarked/marked symbols, a match relation is
introduced, in order to specify when such strings agree. Then a regular set
over the bipartite alphabet can be interpreted as specifying another language
over the unmarked alphabet, called the consensual language. A word is in the
consensual language if a set of corresponding matching strings is in the
original language. The family thus defined includes the regular languages and
also interesting non-semilinear ones. The word problem can be solved in
NLOGSPACE, hence in P time.
The emptiness problem is undecidable.
Closure properties are
proved for intersection with regular sets and inverse alphabetical homomorphism.
Several conditions for a consensual definition to yield a regular language are
presented, and it is shown that the size of a consensual specification of
regular languages can be in a logarithmic ratio with respect to a DFA. The
family is incomparable with context-free and tree-adjoining grammar families.
Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum annealing. We also present preliminary results about the application of quantum dissipation (as an alternative to imaginary time evolution) to the task of driving a quantum system toward its state of lowest energy.
We add sequential operations to the categorical algebra of weighted and
Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra
the algebra permits the description of hierarchical systems, and ones with
evolving geometry. We make a comparison with the probabilistic automata of
Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
We extend the simply typed
λ-calculus with unbind and rebind primitive
constructs. That is, a value can be a fragment of open code,
which in order to be used should be explicitly rebound. This
mechanism nicely coexists with standard static binding. The
motivation is to provide an unifying foundation for mechanisms of
dynamic scoping, where the meaning of a name is
determined at runtime, rebinding, such as dynamic updating
of resources and exchange of mobile code, and delegation,
where an alternative action is taken if a binding is missing.
Depending on the application scenario, we consider two
extensions which differ in the way type safety is guaranteed. The
former relies on a combination of static and dynamic type checking.
That is, rebind raises a dynamic error if for some variable
there is no replacing term or it has the wrong type. In the latter,
this error is prevented by a purely static type system, at the price
of more sophisticated types.
Wang automata are devices for picture language
recognition recently introduced by us, which characterize the class
REC of recognizable picture languages. Thus, Wang automata are
equivalent to tiling systems or online tessellation acceptors, and
are based like Wang systems on labeled Wang tiles. The present work
focus on scanning strategies, to prove that the ones Wang automata
are based on are those following four kinds of movements:
boustrophedonic, “L-like”, “U-like”, and spirals.