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On the fundamental limitations of transformational design
2001
ACM Transactions on Design Automation of Electronic Systems
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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]
2013
Lecture Notes in Computer Science
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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]
2013
arXiv
pre-print
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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]
2016
Communications in Computer and Information Science
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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]
2005
arXiv
pre-print
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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
2006
Journal of Algebra
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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
1982
Theoretical Computer Science
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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
2004
Journal of Symbolic Logic (JSL)
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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]
2019
Green Chemistry and Sustainable Technology
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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
2004
Journal of symbolic computation
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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]
1998
Studies in Logic and the Foundations of Mathematics
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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]
1999
Lecture Notes in Computer Science
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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
1975
Annals of Mathematical Logic
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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
2007
Theory of Computing Systems
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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]
1998
Lecture Notes in Computer Science
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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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