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The Global ETD Search service is a free service for researchers
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Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Showing 1 to 8 of 8 (0.063 seconds)| 1 |
Some Undecidability Results related to the Star Problem in Trace MonoidsKirsten, Daniel 28 November 2012 (has links) (PDF)
This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme from 1994[30,31], we know that the Star Problem is decidable in trace monoids which do not contain a C4-submonoid. The C4 is (isomorphic to) the Caresian Product of two free monoids over doubleton alphabets. It is not known, whether the Star Problem is decidable in C4 or in trace monoids containing a C4. In this paper, we show undecidability of some related problems: Assume a trace monoid which contains a C4. Then, it is undecidable whether for two given recognizable languages K and L, we have K ⊆ L*, although we can decide K* ⊆ L. Further, we can not decide recognizability of K ∩ L* as well as universality and recognizability of K U L*.
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A Connection between the Star Problem and the Finite Power Property in Trace MonoidsKirsten, Daniel 28 November 2012 (has links) (PDF)
This paper deals with a connection between two decision problems for recognizable trace languages: the star problem and the finite power property problem. Due to a theorem by Richomme from 1994 [26, 28], we know that both problems are decidable in trace monoids which do not contain a C4 submonoid. It is not known, whether the star problem or the finite power property are decidable in the C4 or in trace monoids containing a C4.
In this paper, we show a new connection between these problems. Assume a trace monoid IM (Σ, I) which is isomorphic to the Cartesian Product of two disjoint trace monoids IM (Σ1, I1) and IM (Σ2, I2). Assume further a recognizable language L in IM (Σ, I) such that every trace in L contains at least one letter in Σ1 and at least in one letter in Σ2. Then, the main theorem of this paper asserts that L* is recognizable iff L has the finite power property.
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Some Undecidability Results related to the Star Problem in Trace MonoidsKirsten, Daniel 28 November 2012 (has links)
This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme from 1994[30,31], we know that the Star Problem is decidable in trace monoids which do not contain a C4-submonoid. The C4 is (isomorphic to) the Caresian Product of two free monoids over doubleton alphabets. It is not known, whether the Star Problem is decidable in C4 or in trace monoids containing a C4. In this paper, we show undecidability of some related problems: Assume a trace monoid which contains a C4. Then, it is undecidable whether for two given recognizable languages K and L, we have K ⊆ L*, although we can decide K* ⊆ L. Further, we can not decide recognizability of K ∩ L* as well as universality and recognizability of K U L*.
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Two Techniques in the Area of the Star ProblemKirsten, Daniel, Marcinkowski, Jerzy 30 November 2012 (has links) (PDF)
This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by G. Richomme from 1994 [32, 33], we know that the star problem is decidable in trace monoids which do not contain a submonoid of the form {a,c}* x {b,d}*.
Here, we consider a more general problem: Is it decidable whether for some recognizable trace language and some recognizable or finite trace language P the intersection R ∩ P* is recognizable? If P is recognizable, then we show that this problem is decidale iff the underlying trace monoid does not contain a submonoid of the form {a,c}* x b*. In the case of finite languages P, we show several decidability and undecidability results.
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A Connection between the Star Problem and the Finite Power Property in Trace MonoidsKirsten, Daniel 28 November 2012 (has links)
This paper deals with a connection between two decision problems for recognizable trace languages: the star problem and the finite power property problem. Due to a theorem by Richomme from 1994 [26, 28], we know that both problems are decidable in trace monoids which do not contain a C4 submonoid. It is not known, whether the star problem or the finite power property are decidable in the C4 or in trace monoids containing a C4.
In this paper, we show a new connection between these problems. Assume a trace monoid IM (Σ, I) which is isomorphic to the Cartesian Product of two disjoint trace monoids IM (Σ1, I1) and IM (Σ2, I2). Assume further a recognizable language L in IM (Σ, I) such that every trace in L contains at least one letter in Σ1 and at least in one letter in Σ2. Then, the main theorem of this paper asserts that L* is recognizable iff L has the finite power property.
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Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace MonoidsKirsten, Daniel, Richomme, Gwénaël 28 November 2012 (has links) (PDF)
In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the finite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediary results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without C4-submonoid.
We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g. we show the decidability of these problems for recognizable languages which contain at most one non-connected trace.
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Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace MonoidsKirsten, Daniel, Richomme, Gwénaël 28 November 2012 (has links)
In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the finite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediary results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without C4-submonoid.
We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g. we show the decidability of these problems for recognizable languages which contain at most one non-connected trace.
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Two Techniques in the Area of the Star ProblemKirsten, Daniel, Marcinkowski, Jerzy 30 November 2012 (has links)
This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by G. Richomme from 1994 [32, 33], we know that the star problem is decidable in trace monoids which do not contain a submonoid of the form {a,c}* x {b,d}*.
Here, we consider a more general problem: Is it decidable whether for some recognizable trace language and some recognizable or finite trace language P the intersection R ∩ P* is recognizable? If P is recognizable, then we show that this problem is decidale iff the underlying trace monoid does not contain a submonoid of the form {a,c}* x b*. In the case of finite languages P, we show several decidability and undecidability results.
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