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On the fundamental limitations of transformational design

Jeroen Voeten
2001 ACM Transactions on Design Automation of Electronic Systems  
The completeness of a collection of design transformations is an important aspect in transformational design.  ...  In the field of transformational design the problem of incompleteness is not well understood and it is often believed that complete transformation systems can be constructed.  ...  I would further like to thank Leo van Bokhoven and Piet van der Putten for reading and commenting on earlier drafts of this paper, and especially Marc Geilen for contributing to the proofs of the theorems  ... 
doi:10.1145/502175.502181 fatcat:c6k3r5wfofe25ivy7a5d2sui5a

Word Equations with Length Constraints: What's Decidable? [chapter]

Vijay Ganesh, Mia Minnes, Armando Solar-Lezama, Martin Rinard
2013 Lecture Notes in Computer Science  
We show that if word equations can be converted to a solved form, a form relevant in practice, then the satisfiability problem for Boolean combinations of word equations and length constraints is decidable  ...  A corollary of this undecidability result is that this set is undecidable even with sentences with at most two occurrences of a string variable.  ...  This procedure is a sound, complete and terminating procedure for L 0 e,l -formulas whose word equations have effective solved forms.  ... 
doi:10.1007/978-3-642-39611-3_21 fatcat:olludyqgdzhmhexsuzgs4n3qqq

(Un)Decidability Results for Word Equations with Length and Regular Expression Constraints [article]

Vijay Ganesh, Mia Minnes, Armando Solar-Lezama, Martin Rinard
2013 arXiv   pre-print
We show that if word equations can be converted to a solved form, a form relevant in practice, then the satisfiability problem for Boolean combinations of word equations and length constraints is decidable  ...  A corollary of this undecidability result is that this set is undecidable even with sentences with at most two occurrences of a string variable.  ...  This procedure is a sound, complete and terminating procedure for L 0 e,l -formulas whose word equations have effective solved forms.  ... 
arXiv:1306.6054v1 fatcat:53atrdlhi5hr5di7ialhzxcvha

What's Decidable About Parametric Timed Automata? [chapter]

Étienne André
2016 Communications in Computer and Information Science  
On the other hand, restricting the number of clocks, the use of clocks (compared or not with the parameters), and the use of parameters (e. g., used only as upper or lower bounds) leads to decidability  ...  After two decades of research on PTA, it is now well-understood that any non-trivial problem studied is undecidable for general PTA.  ...  A run of a TA is an alternating sequence of states of Q and edges of the form (l 0 , w 0 ) e0 ⇒ (l 1 , w 1 ) e1 ⇒ · · · em−1 ⇒ (l m , w m ), such that for all i = 0, . . . , m − 1, e i ∈ E, and ((l i ,  ... 
doi:10.1007/978-3-319-29510-7_3 fatcat:l6iugmbrjjfnja2oz767fbufaa

Uniform decision problems in automatic semigroups [article]

Mark Kambites, Friedrich Otto (Universitaet Kassel)
2005 arXiv   pre-print
Under the same conditions, we show that one can also decide whether the semigroup is completely simple or completely zero-simple; in the case that it is, one can compute a Rees matrix representation for  ...  the semigroup, in the form of a Rees matrix together with an automatic structure for its maximal subgroup.  ...  If P contains no zero entries, then M (G; I, Λ; P ) is a completely simple semigroup. Conversely, every completely simple or completely zero-simple semigroup is isomorphic to one of this form.  ... 
arXiv:math/0509349v1 fatcat:enr5u4itzva2habo72uox25x2q

Uniform decision problems for automatic semigroups

Mark Kambites, Friedrich Otto
2006 Journal of Algebra  
Under the same conditions, we show that one can also decide whether the semigroup is completely simple or completely zero-simple; in the case that it is, one can compute a Rees matrix representation for  ...  the semigroup, in the form of a Rees matrix together with an automatic structure for its maximal subgroup.  ...  If P contains no zero entries, then M(G; I, Λ; P ) is a completely simple semigroup. Conversely, every completely simple or completely zero-simple semigroup is isomorphic to one of this form.  ... 
doi:10.1016/j.jalgebra.2005.11.028 fatcat:xi5eeodke5bfhjplqmo6huju5i

On the complexity of simple arithmetic expressions

Oscar H. Ibarra, Brian S. Leininger, Shlomo Moran
1982 Theoretical Computer Science  
Let IE be the set of all simple arithmetic expressions of the form E(x) = XT, . . .  ...  VJe show that the inequi\Aence problem (or equivalently, the equivalence problem) for a large subclass of E is decidable in polynomial time.  ...  Acknowledgment We would like to th:mk the referee for suggestions which improved the presentation of the proof of Theorem 4.2.  ... 
doi:10.1016/0304-3975(82)90012-3 fatcat:4h4qr66va5flpee5ayr3btcbly

Degree spectra of prime models

Barbara F. Csima
2004 Journal of Symbolic Logic (JSL)  
Indeed, this is a corollary of the fact that if T is a complete decidable theory and L is a computable set of c.e. partial types of T, then for any degree d > 0, T has a d-decidable model omitting the  ...  If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 < d < 0', there is a prime model with elementary diagram of degree d.  ...  Let T be a complete decidable theory and let L be a computable set Γ of c.e. partial types of T .  ... 
doi:10.2178/jsl/1082418536 fatcat:7wo5gmbzm5govprprscbdmbfwi

Kleene Algebra with Hypotheses [chapter]

Amina Doumane, Denis Kuperberg, Damien Pous, Pierre Pradic
2019 Green Chemistry and Sustainable Technology  
We also answer a question posed by Cohen about hypotheses of the form 1 = S where S is a sum of letters: we show that it is decidable.  ...  While their equational theories coincide and are PSpace-complete, their Horn theories differ and are undecidable.  ...  ≤ f Decidable EXPTIME − complete Σ 0 1 −complete Π 1 1 −complete KA * H e ≤ f Decidable Π 0 1 −complete Π 0 2 −complete Π 1 1 −complete if u[f ]v ⊆ cl H (L) then u[e]v ⊆ cl H (L) .  ... 
doi:10.1007/978-3-030-17127-8_12 dblp:conf/fossacs/DoumaneKPP19 fatcat:ou75emy7ynbujot6wrjbmjulfe

Tractable and intractable second-order matching problems

Kouichi Hirata, Keizo Yamada, Masateru Harao
2004 Journal of symbolic computation  
It is well-known that the second-order matching problem is NP-complete.  ...  The second-order matching problem is the problem of determining, for a finite set { ti, si | i ∈ I} of pairs of a second-order term ti and a first-order closed term si, called a matching expression, whether  ...  Since E c {f (0, w 1 )/F } is of the form { f (0, f(z 3 , f(z 2 , f(z 1 , y)))), f(0, f(0, f(1, Suppose that f (0, f(0, w 1 ))/F ∈ σ.  ... 
doi:10.1016/j.jsc.2003.09.002 fatcat:c3mvlslzrzdbrexciaqbxd6uau

Chapter 1 Pure computable model theory [chapter]

Valentina S. Harizanov
1998 Studies in Logic and the Foundations of Mathematics  
Hence, if Ax is a set of axioms of a theory T , then T is decidable if there is an algorithm which determines for every sentence σ of L, whether Ax'σ.  ...  Peretyat'kin [166] has shown that there is a complete decidable theory T which is neither ℵ 0 -categorical nor ℵ 1 -categorical, and which has, up to isomorphism, a unique decidable model.  ...  I thank Tim McNicholl for proofreading parts of an early draft. I thank Graeme Bailey for technical assistance with word-processing.  ... 
doi:10.1016/s0049-237x(98)80002-5 fatcat:mktikwmmazgale5ejrpnihv6hm

Tractable and Intractable Second-Order Matching Problems [chapter]

Kouichi Hirata, Keizo Yamada, Masateru Harao
1999 Lecture Notes in Computer Science  
It is well-known that the second-order matching problem is NP-complete.  ...  The second-order matching problem is the problem of determining, for a finite set { ti, si | i ∈ I} of pairs of a second-order term ti and a first-order closed term si, called a matching expression, whether  ...  Since E c {f (0, w 1 )/F } is of the form { f (0, f(z 3 , f(z 2 , f(z 1 , y)))), f(0, f(0, f(1, Suppose that f (0, f(0, w 1 ))/F ∈ σ.  ... 
doi:10.1007/3-540-48686-0_43 fatcat:kif2eqafhvcnvnbrfqbawgsgmm

Decidability results in non-classical logics

Dov M. Gabbay
1975 Annals of Mathematical Logic  
L is complete for the class M of all Kripke structures of HPC of the form (T, Pl , ~, Ut <t) ~vhere: (a) TC_{x~ w*lOolx}; (b)y E T^ x~l y-~ xE T;(c) (U t, <t), t E T is a totally linearly ordered countable  ...  (c) (A, 0) is said tc be complete (in a certain language) iff for all ~ff A of this language, either A E A or A E 0.  ...  Our first results is the decidability of an ~ntuitioristic tense syster ~ ! t.  ... 
doi:10.1016/0003-4843(75)90004-2 fatcat:joo3erigrbeqdim6ghxjxlqlgm

Partial Bi-immunity, Scaled Dimension, and NP-Completeness

John M. Hitchcock, A. Pavan, N. V. Vinodchandran
2007 Theory of Computing Systems  
In this paper we separate the same NP-completeness notions under a partial bi-immunity hypothesis that is weaker and only yields a language in NP that is hard to solve on most strings.  ...  The proofs of all these results rely on the existence of a language in NP with almost everywhere hardness.  ...  Machine M Le (x) 1 if |x| is not of the form t 2i 2 then simulate the deterministic machine for L e and decide. 3 n ← |x|; 4 l 0 , l 1 , l 2 ← λ; /* Initialize lists to the root of T x */ 5 while |l i  ... 
doi:10.1007/s00224-007-9000-2 fatcat:27wcw5k5lbajbahxd7oeem7agi

The decidability of simultaneous rigid E-unification with one variable [chapter]

Anatoli Degtyarev, Yuri Gurevich, Paliath Narendran, Margus Veanes, Andrei Voronkov
1998 Lecture Notes in Computer Science  
We show that simultaneous rigid E-uni cation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable.  ...  This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable.  ...  Decidability of monadic SREU 25]. 2. Decidability of SREU with two rigid equations. Both problems are highly non-trivial.  ... 
doi:10.1007/bfb0052370 fatcat:m2i2lqsppnbbxe4ntkktlihfkq
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