Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

We show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring. A max-plus tree automaton is called finitely ambiguous if the number of accepting runs on every tree is bounded by a global constant. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton

Register complexity and determinisation of max-plus automata

We survey some results about the sequentiality problem for max-plus automata and its generalisation, the register complexity problem for cost register automata. We compare classes of functions computed by maxplus automata and by cost register automata with respect to the notion of ambiguity. The two models are introduced gently, so the novice reader is welcome

Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic. We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete

Factory of realities: on the emergence of virtual spatiotemporal structures

The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these "realities" real? Which "physics" should be applied to quantitatively describe them? In this essay I dwell on few examples. The first is Adaptive neural networks, which are not networks and not neural, but still provide service similar to classical ANNs in extended fashion. The second is the emergence of objects looking like Einsteinian spacetime, which describe the behavior of an Internet surfer like geodesic motion. The third is the demonstration of nonclassical and even stronger-than-quantum probabilities in Information Retrieval, their use. Immense operable datasets provide new operationalistic environments, which become to greater and greater extent "realities". In this essay, I consider the overall Information Retrieval process as an objective physical process, representing it according to Melucci metaphor in terms of physical-like experiments. Various semantic environments are treated as analogs of various realities. The readers' attention is drawn to topos approach to physical theories, which provides a natural conceptual and technical framework to cope with the new emerging realities.Comment: 21 p

Regular Methods for Operator Precedence Languages

The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time

Computation in Finitary Stochastic and Quantum Processes

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and generators are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated beam splitter, an atom in a magnetic field, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that these systems' behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous corrections and update

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Graph-based software specification and verification

The (in)correct functioning of many software systems heavily influences how\ud we qualify our daily lives. Software companies as well as academic computer\ud science research groups spend much effort on applying and developing techniques for improving the correctness of software systems. In this dissertation\ud we focus on using and developing graph-based techniques to specify and verify\ud the behaviour of software systems in general, and object-oriented systems more\ud specifically. We elaborate on two ways to improve the correctness (and thereby\ud the quality) of such systems.\ud Firstly, we investigate the potential of using the graph transformation tech-\ud nique to formally specify the dynamic semantics of (object-oriented) program-\ud ming languages. Those semantics are typically specified in natural language.\ud Such specifications are often hard to understand or even ambiguous. We show\ud how the graph transformation framework provides formal and intuitive means\ud for their specification.\ud Secondly, we develop techniques to verify systems of which the behaviour is\ud specified as graph production systems. For the verification of such systems, we\ud introduce an algorithm that combines a well-known on-the-\ud y model checking\ud algorithm with ideas from bounded model checking. One of the main prob-\ud lems of model checking is the state-explosion problem. This problem is often\ud tackled using partial order reduction techniques. Unfortunately, many such\ud techniques are based on assumptions that do not hold for graph production sys-\ud tems. Therefore, we develop a new dynamic partial order reduction algorithm\ud based on selecting so-called probe sets and prove its correctness.\ud Most of the techniques developed in this dissertation have been implemented\ud in the graph transformation tool GROOVE