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28
A Strict Border for the Decidability of EUnification for Recursive Functions
, 1998
"... During the execution of functional logic programs, Eunification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability of those Eunification problems? Up to now, there does not exist a concrete answer ..."
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During the execution of functional logic programs, Eunification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability of those Eunification problems? Up to now, there does not exist a concrete answer to this question for classes of equational theories which are induced by particular recursive functions. In this paper, we try to give an answer to this question by drawing and verifying a strict border between undecidability and decidability of Eunification problems for particular classes of recursive functions. Since this result shows that the Eunification problem is undecidable even for a very restricted class of recursive functions, the nondeterministic implementations of those problems in functional logic programming languages are justified.
Compositions of Topdown Tree Transducers with "rules
"... Abstract. Topdown tree transducers with "rules ("tdtt) are a restricted version of extended topdown tree transducers. They are implemented in the framework Tiburon and ful ll some criteria desirable in a machine translation model. However, they compute a class of transformations that is ..."
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Abstract. Topdown tree transducers with "rules ("tdtt) are a restricted version of extended topdown tree transducers. They are implemented in the framework Tiburon and ful ll some criteria desirable in a machine translation model. However, they compute a class of transformations that is not closed under composition (not even for linear and nondeleting "tdtt). A composition construction that composes "tdtt M and N is presented. It is correct whenever (i) M has at most one output symbol in each rule, (ii) M is deterministic or N is linear, and (iii) M is total or N is nondeleting. This corresponds nicely to a classical composition result by Baker. 1
Compositions of bottomup tree series transformations
 UNIVERSITY OF SZEGED
, 2005
"... Tree series transformations computed by bottomup tree series transducers are called bottomup tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottomup tree series transformations over commutative and ...complete semirings are clos ..."
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Tree series transformations computed by bottomup tree series transducers are called bottomup tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottomup tree series transformations over commutative and ...complete semirings are closed under leftcomposition with linear bottomup tree series transformations and rightcomposition with boolean deterministic bottomup tree series transformations.
Hierarchies of Tree Series Transformations Revisited
, 2006
"... Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutativ ..."
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Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izzsemirings (izz abbreviates idempotent, zerosum and zerodivisor free) is generalized to arbitrary positive (i. e., zerosum and zerodivisor free) commutative semirings. The latter class of semirings includes prominent examples such as the natural numbers semiring and the least common multiple semiring, which are not members of the former class.
Cutoffs and Automata in Formal Verification of InfiniteState Systems
, 2006
"... In this habilitation thesis, we discuss two complementary approaches to formal verification of infinitestate systems—namely, the use cutoffs and automatabased symbolic model checking (especially the socalled regular model checking). The thesis is based on extended versions of multiple conference ..."
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In this habilitation thesis, we discuss two complementary approaches to formal verification of infinitestate systems—namely, the use cutoffs and automatabased symbolic model checking (especially the socalled regular model checking). The thesis is based on extended versions of multiple conference and journal papers joint into a unified framework and accompanied with a significantly extended overview of other existing approaches. The presented original results include cutoffs for verification of parameterised networks of processes with shared resources, the approach of abstract regular model checking combining regular model checking with the counterexampleguided abstraction refinement (CEGAR) loop, a proposal of using language inference for regular model checking, techniques for an application of regular model checking to verification of programs manipulating dynamic linked data structures, the approach of abstract regular tree model checking as well as a proposal of a novel class of tree automata with size constraints with applications in verification of programs manipulating balanced tree structures.
TreeSeriestoTreeSeries Transformations
, 2008
"... We investigate the treeseriestotreeseries (tsts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not welldefined. In practice, many used semirings are not complete (like the probability semiring). We establish a syn ..."
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We investigate the treeseriestotreeseries (tsts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not welldefined. In practice, many used semirings are not complete (like the probability semiring). We establish a syntactical condition that guarantees welldefinedness of the tsts transformation in arbitrary commutative semirings. For positive (i. e., zerosum and zerodivisor free) semirings the condition actually characterizes the welldefinedness, so that welldefinedness is decidable in this scenario.
Compositions of Tree Series Transformations ⋆ Abstract
"... Tree series transformations computed by bottomup and topdown tree series transducers are called bottomup and topdown tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottomup tree series transformations ..."
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Tree series transformations computed by bottomup and topdown tree series transducers are called bottomup and topdown tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottomup tree series transformations over a commutative and complete semiring is closed under leftcomposition with linear bottomup tree series transformations and rightcomposition with boolean deterministic bottomup tree series transformations. Moreover, it is shown that the class of topdown tree series transformations over a commutative and complete semiring is closed under rightcomposition with linear, nondeleting topdown tree series transformations. Finally, the composition of a boolean, deterministic, total topdown tree series transformation with a linear topdown tree series transformation is shown to be a topdown tree series transformation. Key words: tree series transformation, semiring, composition, tree transducer 1
Incomparability Results for Classes of Polynomial Tree Series Transformations
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Branching Synchronization Grammars with Nested Tables
, 2002
"... A generalization of ET0L systems is introduced: grammars with branching synchronization and nested tables. Branching synchronization grammars with tables of nesting depth n have the same string and treegenerating power as nfold compositions of topdown tree transducers. ..."
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A generalization of ET0L systems is introduced: grammars with branching synchronization and nested tables. Branching synchronization grammars with tables of nesting depth n have the same string and treegenerating power as nfold compositions of topdown tree transducers.
INFINITY 2005 Preliminary Version Abstract Regular Tree Model Checking
"... Regular (tree) model checking (RMC) is a promising generic method for formal verification of infinitestate systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the system ..."
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Regular (tree) model checking (RMC) is a promising generic method for formal verification of infinitestate systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the systems being examined as finite word or tree transducers. The reachability set is then computed by a repeated application of the transducers on the automata representing the currently known set of reachable configurations. In order to facilitate termination of RMC, various acceleration schemas have been proposed. One of them is a combination of RMC with the abstractcheckrefine paradigm yielding the socalled abstract regular model checking (ARMC). ARMC has originally been proposed for word automata and transducers only and thus for dealing with systems with linear (or easily linearisable) structure. In this paper, we propose a generalisation of ARMC to the case of dealing with trees which arise naturally in a lot of modelling and verification contexts. In particular, we first propose abstractions of tree automata based on collapsing their states having an equal language of trees up to some bounded height. Then, we propose an abstraction based on collapsing states having a nonempty intersection (and thus “satisfying”) the same bottomup tree “predicate ” languages. Finally, we show on several examples that the methods we propose give us very encouraging verification results. 1