Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete

Logico-numerical max-strategy iteration

Strategy iteration methods are used for solving fixed point equations. It has been shown that they improve precision in static analysis based on abstract interpretation and template abstract domains, e.g. intervals, octagons or template polyhedra. However, they are limited to numerical programs. In this paper, we propose a method for applying max-strategy iteration to logico-numerical programs, i.e. programs with numerical and Boolean variables, without explicitly enumerating the Boolean state space. The method is optimal in the sense that it computes the least fixed point w.r.t. the abstract domain; in particular, it does not resort to widening. Moreover, we give experimental evidence about the efficiency and precision of the approach

Molecular analysis of phosphoglycerate kinase in Trypanoplasma borreli and the evolution of this enzyme in kinetoplastida.

In the protozoan kinetoplastid organism Trypanoplasma borreli, phosphoglycerate kinase (PGK) activity was found in two different cell compartments: 80% in the cytosol and 20% in peroxisome-like organelles called glycosomes. However, only one functional pgk gene could be detected, in addition to a pseudo-pgk gene. No short-range linkage could be established between these two genes, although they are presumably present on the same chromosome. The intact gene codes for a polypeptide of 411 amino acids, with a C-terminal extension of four residues, -VAKF, a sequence with probably a low targeting efficiency for glycosomes. The calculated net charge and molecular mass of the encoded polypeptide are +13 and 44230Da, respectively. In other Kinetoplastida, different tandemly arranged genes code for distinct PGK isoenzymes in glycosomes and cytosol. By comparison of the pgk gene organization, and a phylogenetic analysis, we have traced a plausible scenario of the evolution of the PGK isoenzymes in these organisms and of the enzymes' intracellular compartmentation

Organization, sequence and stage-specific expression of the phosphoglycerate kinase genes of Leishmania mexicana mexicana

In Leishmania mexicana two genes were detected coding for different isoforms of the glycolytic enzyme phosphoglycerate kinase. This situation contrasts with that observed in other Trypanosomatidae (Trypanosoma brucei, Trypanosoma congolense, Crithidia fasciculata) analyzed previously, which all contain three different genes coding for isoenzymes A, B and C, respectively. All attempts to detect in L. mexicana a type A PGK, or a gene encoding it, proved unsuccesful. We have cloned and characterized the genes PGKB and PGKC. They code for polypeptides of 416 and 478 amino acids with a molecular mass of 45146 and 51318 Da, respectively. The two polypeptides are 99% identical. PGKC is characterized by a 62 residue C-terminal extension with alternating stretches of hydrophobic and charged, mainly positive amino acids. As in other Trypanosomatidae, PGKB is located in the cytosol, PGKC in the glycosomes. However, Leishmania mexicana distinguishes itself from other trypanosomatids by the simultaneous expression of these isoenzymes: approximately 80% of PGK activity is found in the cytosol and 20% in the glycosomes, both in promastigotes and in the amastigote-like form of the parasite

Abstract interpretation meets convex optimization

Special issue on Invariant generation and reasoning about loops.International audienc

The expression and intracellular distribution of phosphoglycerate kinase isoenzymes in Trypanosoma cruzi

In this paper, we report the subcellular distribution of phosphoglycerate kinase (PGK) in epimastigotes of Trypanosoma cruzi. Approximately 80% of the PGK activity was found in the cytosol, 20% in the glycosomes. Western blot analysis suggested that two isoenzymes of 56 and 48 kDa, respectively, are responsible for the glycosomal PGK activity, whereas the cytosolic activity should be attributed to a single PGK of 48 kDa. In analogy to the situation previously reported for PGK in Trypanosoma brucei, these isoenzymes were called PGKA, C and B, respectively. However, in T. cruzi, PGKA seems not to be a minor enzyme like its counterpart in T. brucei. Whereas PGKC behaved as a soluble glycosomal matrix protein, PGKA appeared to be present at the inner surface of the organelle's membrane. After alkaline carbonate treatment, the enzyme remained associated with the particulate fraction of the organelles. Upon solubilization of glycosomes with Triton X-114, PGKA was recovered from the detergent phase, indicating its (partial) hydrophobic character and therefore, a possible hydrophobic interaction with the membrane. The PGKA gene was cloned and sequenced, but the predicted amino-acid sequence did not reveal an obvious clue as to the mechanism by which the enzyme is attached to the glycosomal membrane, (C) 2001 Elsevier Science B.V. All rights reserved